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Start Over Descriptor "14L15" Journal journal of algebra
5 results on '"14L15"'

1. On functor points of affine supergroups.

Author

Masuoka, Akira and Shibata, Taiki

Subjects
*SUPERALGEBRAS, *FUNCTOR theory, *MATHEMATICAL decomposition, *COCYCLES
Abstract

To construct an affine supergroup from a Harish-Chandra pair, Gavarini [2] invented a natural method, which first constructs a group functor and then proves that it is representable. We give a simpler and more conceptual presentation of his construction in a generalized situation, using Hopf superalgebras over a superalgebra. As an application of the construction, given a closed super-subgroup of an algebraic supergroup, we describe the normalizer and the centralizer, using Harish-Chandra pairs. We also prove a tensor product decomposition theorem for Hopf superalgebras, and describe explicitly by cocycle deformation, the difference which results from the two choices of dualities found in literature. [ABSTRACT FROM AUTHOR]

Published
2018
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2. Generalized 1-motivic sheaves.

Author

Bertapelle, A.

Subjects
*SHEAF theory, *GENERALIZABILITY theory, *ALGEBRAIC field theory, *GROUP theory, *QUOTIENT rule
Abstract

Let k be a field of characteristic 0. We extend the definition of the category of 1-motivic sheaves, introduced by Barbieri-Viale and Kahn, allowing quotients of connected algebraic k -groups by formal k -groups. We show that its bounded derived category is equivalent to the bounded derived category of the category of generalized 1-motives with torsion. [ABSTRACT FROM AUTHOR]

Published
2014
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3. Principal bundles, quasi-abelian varieties and structure of algebraic groups

Author

Fernando Sancho de Salas and Carlos Sancho de Salas

Subjects
Discrete mathematics, Abelian variety, Quasi-abelian varieties, Pure mathematics, Algebra and Number Theory, Elementary abelian group, Reductive group, Principal bundles, Algebraic groups, Free abelian group, Mathematics - Algebraic Geometry, Group scheme, Algebraic group, Affine group, FOS: Mathematics, Affine variety, Algebraic Geometry (math.AG), 14L15, Mathematics
Abstract

We classify principal bundles over anti-affine schemes with affine and commutative structural group. We show that this yields the classification of quasi-abelian varieties over a field k (i.e., group k-schemes with no non constant global functions). The interest of this result is given by the fact that the classification of smooth group k-schemes is reduced to the classification of quasi-abelian varieties and of certain affine group schemes., Comment: 26 pages

Published
2009

4. Fundamental group schemes for stratified sheaves

Author

João Pedro Pinto dos Santos, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)

Subjects
Abelian variety, Algebra and Number Theory, Differential equations in positive characteristic, 010102 general mathematics, Elementary abelian group, Unipotent, 01 natural sciences, Ground field, Free abelian group, [ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG], Algebra, Mathematics::Algebraic Geometry, Fundamental groups, Group scheme, Abelian varieties, Scheme (mathematics), Mathematics::Category Theory, 0103 physical sciences, 010307 mathematical physics, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], 0101 mathematics, Abelian group, Mathematics::Representation Theory, 14L15, Mathematics
Abstract

International audience; We study stratified sheaves in positive characteristic algebraic geometry using the technique of Tannakian categories. We show that the associated Tannakian group scheme Π is a perfect scheme. We also prove that in the proper case the largest unipotent quotient of Π is pro-etale. Special attention is paid to abelian varieties, where a description of Π is obtained. We finish with a discussion of the case where the ground field is valued

Published
2007
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5. Locally trivial principal homogeneous spaces and conjugacy theorems for Lie algebras

Author

Arturo Pianzola

Subjects
Pure mathematics, Real form, 01 natural sciences, Representation theory, 17B01, Mathematics - Algebraic Geometry, Conjugacy class, 0103 physical sciences, FOS: Mathematics, Trivial representation, Representation Theory (math.RT), 0101 mathematics, Abelian group, Mathematics::Representation Theory, Algebraic Geometry (math.AG), Mathematics, Discrete mathematics, Algebra and Number Theory, Simple Lie group, 010102 general mathematics, Mathematics::Rings and Algebras, 16. Peace & justice, Lie conformal algebra, 14L15, Adjoint representation of a Lie algebra, 010307 mathematical physics, Mathematics - Representation Theory
Abstract

For g a split semisimple Lie algebra over a field of characteristic 0, we link locally trivial principal homogeneous spaces over Spec(R) to the question of conjugacy of maximal abelian diagonalizable subalgebras of g(R)., 18 pages, to appear in Journal of Algebra

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