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61. Generalized skew derivations on semiprime rings.

Author

De Filippis, Vincenzo and Di Vincenzo, Onofrio Mario

Subjects
*SEMIRINGS (Mathematics), *QUOTIENT rings, *GENERALIZED spaces, *INTEGERS, *AUTOMORPHISMS
Abstract

Letbe a semiprime ring with centre,its right Martindale quotient ring,its extended centroid,a generalized skew derivation of, associated with a non-zero skew derivationof, andfixed integers such that, for all. Thencontains a non-zero central ideal. The case of centralizers (generalized skew derivations associated with a zero skew derivation) is also studied. [ABSTRACT FROM AUTHOR]

Published
2015
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69. Robinson–Schensted–Knuth Correspondence and Weak Polynomial Identities of M1,1(E).

Author

di Vincenzo, Onofrio Mario and la Scala, Roberto

Subjects
*POLYNOMIALS, *SUPERALGEBRAS, *HILBERT algebras, *NONASSOCIATIVE algebras, *FUNCTIONAL analysis, *MATHEMATICAL analysis
Abstract

In this paper, it is proved that the ideal Iw of the weak polynomial identities of the superalgebra M1,1(E) is generated by the proper polynomials [x1, x2, x3] and [x2, x1] [x3, x1] [x4, x1]. This is proved for any infinite field F of characteristic different from 2. Precisely, if B is the subalgebra of the proper polynomials of F, we determine a basis and the dimension of any multihomogeneous component of the quotient algebra B / (B ∩ Iw). We also compute the Hilbert series of this algebra. One of the main tools of this paper is a variant we found of the Robinson–Schensted–Knuth correspondence defined for single semistandard tableaux of double shape. [ABSTRACT FROM AUTHOR]

Published
2005
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70. <f>Z2</f>-graded cocharacters for superalgebras of triangular matrices

Author

Di Vincenzo, Onofrio M. and Nardozza, Vincenzo

Subjects
*ALGEBRA, *POLYNOMIALS, *MATRICES (Mathematics), *MATHEMATICS
Abstract

Let K be a field of characteristic zero, let A, B be K-algebras with polynomial identity and let M be a free (A,B)-bimodule. The algebra R=A/0 M/B can be endowed with a natural Z2-grading. In this paper, we compute the graded cocharacter sequence, the graded codimension sequence and the superexponent of R. As a consequence of these results, we also study the above PI-invariants in the setting of upper triangular matrices. In particular, we completely classify the algebra of 3×3 upper triangular matrices endowed with all possible Z2-gradings. [Copyright &y& Elsevier]

Published
2004
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71. ALGEBRAS SATISFYING THE POLYNOMIAL IDENTITY [x1,x2][x3,x4,x5]=0.

Author

di Vincenzo, Onofrio M., Drensky, Vesselin, and Nardozza, Vincenzo

Subjects
*PI-algebras, *ALGEBRA, *MATHEMATICS, *ASSOCIATIVE algebras, *MATRICES (Mathematics)
Abstract

Let ${\mathbb K}$ be a field of characteristic zero, and ${\mathfrak M}_5$ the variety of associative unitary algebras defined by the polynomial identity [x1,x2][x3,x4,x5]=0. This variety is one of the several minimal varieties of exponent 3 (and all proper subvarieties are of exponents 1 and 2). We describe asymptotically its proper subvarieties. More precisely, we define certain algebras ℛ2k for any k∈ℕ and show that if ${\mathfrak U}$ is a proper subvariety of ${\mathfrak M}_5$, then the T-ideal of its polynomial identities is asymptotically equivalent to the T-ideal of the identities of one of the algebras ${\mathbb K}$, E, ℛ2k or ℛ2k⊕E, for a suitable k∈ℕ. We give also another description relating the T-ideals of the proper subvarieties of ${\mathfrak M}_5$ with the polynomial identities of upper triangular matrices of a suitable size. [ABSTRACT FROM AUTHOR]

Published
2004
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74. On the ∗-polynomial identities of M1,1(E)

Author

Di Vincenzo, Onofrio M. and Koshlukov, Plamen

Abstract

In this paper we consider the algebra M1,1(E) endowed with the involution ∗ induced by the transposition superinvolution of the superalgebra M1,1(F) of 2×2-matrices over the field F. We study the ∗-polynomial identities for this algebra in the case of characteristic zero. We describe a finite set generating the ideal of its ∗-identities. We also consider Mn(E), the algebra of n×n matrices over the Grassmann algebra E. We prove that for a large class of involutions defined on it any ∗-polynomial identity is indeed a polynomial identity. A similar result holds for the verbally prime algebra Mk,l(E).

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75. On Z2-graded polynomial identities of the Grassmann algebra

Author

Di Vincenzo, Onofrio M. and da Silva, Viviane Ribeiro Tomaz

Subjects
Grassmann algebra, Mathematics::Commutative Algebra, Cocharacters, Graded polynomial identities, Codimensions
Abstract

Let F be a field of characteristic zero and let E be the Grassmann algebra of an infinite dimensional F-vector space L. In this paper we study the Z2-graded polynomial identities of E with respect to any fixed Z2-grading such that L is an homogeneous subspace. We found explicit generators for the ideal, T2(E), of graded polynomial identities of E and we determine its cocharacter and codimension sequences.

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77. Derived Lengths of Symmetric Poisson Algebras

Author

Siciliano, Salvatore, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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78. Group and Polynomial Identities in Group Rings

Author

Spinelli, Ernesto, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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79. Regev’s Conjecture for Algebras with Hopf Actions

Author

Berele, Allan, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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80. Graded Algebras, Algebraic Functions, Planar Trees, and Elliptic Integrals

Author

Drensky, Vesselin, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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81. Relatively Free Algebras of Finite Rank

Author

Mello, Thiago Castilho de, Yasumura, Felipe Yukihide, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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82. Computing Multiplicities in the Sign Trace Cocharacters of M 2,1(F)

Author

Carini, Luisa, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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83. b-Generalized Skew Derivations on Multilinear Polynomials in Prime Rings

Author

Filippis, Vincenzo De, Scudo, Giovanni, Wei, Feng, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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84. On the Asymptotics of Capelli Polynomials

Author

Benanti, Francesca Saviella, Valenti, Angela, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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85. Minimal Degree of Identities of Matrix Algebras with Additional Structures

Author

Bessades, Dafne, Santos, Rafael Bezerra dos, Vieira, Ana Cristina, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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86. ℓ-Weak Identities and Central Polynomials for Matrices

Author

Blachar, Guy, Matzri, Eli, Rowen, Louis, Vishne, Uzi, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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87. Growth of Differential Identities

Author

Rizzo, Carla, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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88. Cayley Hamilton Algebras

Author

Procesi, Claudio, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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89. Some Thoughts on the Current State of the Theory of Identical Relations in Lie Algebras

Author

Bahturin, Yuri, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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90. Notes on the History of Identities on Group (and Loop) Algebras

Author

Milies, C. Polcino, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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91. Identities in Group Rings, Enveloping Algebras and Poisson Algebras

Author

Petrogradsky, Victor, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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92. On Almost Nilpotent Varieties of Linear Algebras

Author

Mishchenko, Sergey P., Valenti, Angela, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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93. (δ, ε)-Differential Identities of UT m (F)

Author

Nardozza, Vincenzo C., Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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94. Context-Free Languages and Associative Algebras with Algebraic Hilbert Series

Author

La Scala, Roberto, Piontkovski, Dmitri, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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95. Codimension Growth for Weak Polynomial Identities, and Non-integrality of the PI Exponent

Author

Koshlukov, Plamen, Macêdo, David Levi da Silva, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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96. On Codimensions of Algebras with Involution

Author

La Mattina, Daniela, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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97. Central Polynomials of Algebras and Their Growth

Author

Giambruno, Antonio, Zaicev, Mikhail, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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98. Trace Identities on Diagonal Matrix Algebras

Author

Ioppolo, Antonio, Koshlukov, Plamen, La Mattina, Daniela, Alberti, Giovanni, Series Editor, Patrizio, Giorgio, Editor-in-Chief, Bracci, Filippo, Series Editor, Canuto, Claudio, Series Editor, Ferone, Vincenzo, Series Editor, Fontanari, Claudio, Series Editor, Moscariello, Gioconda, Series Editor, Pistoia, Angela, Series Editor, Sammartino, Marco, Series Editor, Di Vincenzo, Onofrio Mario, editor, and Giambruno, Antonio, editor

Published
2021
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99. Propriedade Specht e série de Hilbert racional para superálgebras com superinvolução e álgebras com ação de álgebra de Hopf

Author

Estrada Serna, Alejandro, 1993, Lopatin, Artem, 1980, Centrone, Lucio, 1983, Kochloukov, Plamen Emilov, Kanel-Belov, Alexei, Di Vincenzo, Onofrio Mario, Universidade Estadual de Campinas. Instituto de Matemática, Estatística e Computação Científica, Programa de Pós-Graduação em Matemática, and UNIVERSIDADE ESTADUAL DE CAMPINAS

Subjects
Cocharacter, Graded algebras, Hopf algebras, PI-álgebras, Álgebra de Hopf, Álgebras graduadas, Co-caracter, PI-algebras
Abstract

Orientadores: Artem Lopatin, Lucio Centrone Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica Resumo: Um dos principais problemas na PI-teoria é provar a propriedade de Specht para uma determinada álgebra e provar a racionalidade da série de Hilbert da álgebra relativamente livre. Nesta tese de doutorado consideramos um corpo F de característica 0 e provamos a propriedade Specht para a variedade de superalgebras com superinvolução finitamente gerada sobre F e para a variedade de álgebras H_m-módulo geradas pela álgebra UT_2(F) de matrizes triangulares superiores 2 x 2 onde H_m é uma álgebra de Taft de dimensão m^2. Alem disso, provamos a racionalidade da série de Hilbert da PI-álgebra A sobre F tanto no caso A sendo uma superalgebra com superinvolução como no caso de uma álgebra de Hopf semisimples de dimensão finita agindo sobre A Abstract: One of the main problems in PI-theory is to prove the Specht property for a given algebra and the rationality of the Hilbert series of its relatively free algebra. In this doctoral thesis we consider a field F of characteristic 0 and we prove the Specht property for the variety of finitely generated superalgebras with superinvolution over F and for the variety of H_m-module algebras generated by the algebra UT_2(F) of 2 x 2 upper triangular matrices, where H_m is a Taft's Hopf algebra of dimension m^2. Moreover, we prove the rationality of the Hilbert series of the PI-algebra A over F both in the case A is a superalgebra with superinvolution and when a finite dimensional semisimple Hopf algebra acts on A Doutorado Matemática Doutor em Matemática CAPES 001

Published
2022

100. Graduações por grupo nas álgebras de matrizes triangulares e identidades graduadas de álgebras universais

Author

Yasumura, Felipe Yukihide, 1991, Kochloukov, Plamen Emilov, 1958, Bahturin, Yuri, Di Vincenzo, Onofrio Mario, Aljadeff, Eli, La Mattina, Daniela, Chestakov, Ivan, Universidade Estadual de Campinas. Instituto de Matemática, Estatística e Computação Científica, Programa de Pós-Graduação em Matemática, and UNIVERSIDADE ESTADUAL DE CAMPINAS

Subjects
Upper triangular matrices, Graded algebras, Identidades polinomiais graduadas, Álgebras graduadas, Graded polynomial identities, Matrizes triangulares superiores
Abstract

Orientadores: Plamen Emilov Kochloukov, Yuri Bahturin Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica Resumo: Nesta tese, classificamos as graduações por um grupo nas álgebras triangulares superiores, vistas como álgebras de Lie e de Jordan, sobre um corpo arbitrário e um grupo arbitrário. À partir deste resultado, e assumindo condições mais fortes, obtivemos a classificação das graduações por um grupo na álgebra das matrizes triangulares em blocos, vista como uma álgebra de Lie e de Jordan. Nós calculamos o comportamento assintótico da sequência de codimensões graduadas de cada gradução na álgebra associativa de matrizes triangulares superiores. Obtemos um resultado parcial para a sequência de codimensões graduadas, para as graduações elementares no caso de Lie. Para as demais graduações nos casos de Lie e Jordan, fomos capazes de calcular o seu expoente graduado. Finalmente, investigamos o problema de determinar uma álgebra simples à partir de suas identidades polinômiais. Nós provamos que $\Omega$-álgebras de dimensão finita graduadas, que são graduadas-primas, sobre um corpo algebricamente fechado, são unicamente determinadas por suas identidades polinomiais graduadas Abstract: In this thesis, we classify group gradings on the algebra of upper triangular matrices, viewed as Lie and Jordan algebras, over an arbitrary field and arbitrary grading group. Using this result, and assuming stronger conditions, we were able to obtain the classification of group gradings on the algebra of block-triangular matrices, viewed as Lie and Jordan algebras. We compute the asymptotic behavior of the graded codimension sequence for any grading on the associative algebra of upper-triangular matrices. For the Lie case, we obtain a partial result for the asymptotic behavior of graded codimensions, and we compute the graded exponent of all gradings on the upper triangular matrices, as Lie and Jordan algebras. Finally, we investigate the problem of determining a simple algebra by its polynomial identities. We prove that finite-dimensional graded $\Omega$-algebras, which are graded-prime, over an algebraically closed field are uniquely determined by their graded polynomial identities Doutorado Matemática Doutor em Matemática FAPESP 2013/22.802-1, 2017/11.018-9

Published
2018

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