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Start Over Descriptor "Hopf algebra" Publisher springer international publishing
107 results on '"Hopf algebra"'

8. Principal Fiber Bundles in Non-commutative Geometry

Author

Kassel, Christian, Dito, Giuseppe, Series editor, Frenkel, Edward, Series editor, Gukov, Sergei, Series editor, Kawahigashi, Yasuyuki, Series editor, Kontsevich, Maxim, Series editor, Landsman, Nicolaas P., Series editor, Cardona, Alexander, editor, Morales, Pedro, editor, Ocampo, Hernán, editor, Paycha, Sylvie, editor, and Reyes Lega, Andrés F., editor

Published
2017
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16. Feynman Graphs

Author

Yeats, Karen, Berestycki, Nathanaël, Series editor, Dafermos, Mihalis, Series editor, Eguchi, Tohru, Series editor, Kuniba, Atsuo, Series editor, Marcolli, Matilde, Series editor, Nachtergaele, Bruno, Series editor, and Yeats, Karen

Published
2017
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17. The Connes-Kreimer Hopf Algebra

Author

Yeats, Karen, Berestycki, Nathanaël, Series editor, Dafermos, Mihalis, Series editor, Eguchi, Tohru, Series editor, Kuniba, Atsuo, Series editor, Marcolli, Matilde, Series editor, Nachtergaele, Bruno, Series editor, and Yeats, Karen

Published
2017
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18. Combinatorial Classes and Rooted Trees

Author

Yeats, Karen, Berestycki, Nathanaël, Series editor, Dafermos, Mihalis, Series editor, Eguchi, Tohru, Series editor, Kuniba, Atsuo, Series editor, Marcolli, Matilde, Series editor, Nachtergaele, Bruno, Series editor, and Yeats, Karen

Published
2017
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19. Multiple Zeta Values

Author

Huber, Annette, Müller-Stach, Stefan, Ambrosio, Luigi, Series editor, Baladi, Viviane, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Huisken, Gerhard, Series editor, Jost, Jürgen, Series editor, Kollar, Janos, Series editor, Laumon, Gérard, Series editor, Tillmann, Ulrike, Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, Huber, Annette, Müller-Stach, Stefan, Friedrich, Benjamin, With contrib. by, and von Wangenheim, Jonas, With contrib. by

Published
2017
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23. Kitaev’s Quantum Double Model from a Local Quantum Physics Point of View

Author

Naaijkens, Pieter, Dito, Giuseppe, Series editor, Frenkel, Edward, Series editor, Gukov, Sergei, Series editor, Kawahigashi, Yasuyuki, Series editor, Kontsevich, Maxim, Series editor, Landsman, Nicolaas P., Series editor, Brunetti, Romeo, editor, Dappiaggi, Claudio, editor, Fredenhagen, Klaus, editor, and Yngvason, Jakob, editor

Published
2015
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24. Information Algebras and Their Applications

Author

Marcolli, Matilde, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Nielsen, Frank, editor, and Barbaresco, Frédéric, editor

Published
2015
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25. Braided Hopf Algebras

Author

Kharchenko, Vladislav, Morel, J.-M., Editor-in-chief, Teissier, Bernard, Editor-in-chief, De Lellis, Camillo, Series editor, di Bernardo, Mario, Series editor, Figalli, Alessio, Series editor, Khoshnevisan, Davar, Series editor, Kontoyiannis, Ioannis, Series editor, Lugosi, Gabor, Series editor, Podolskij, Mark, Series editor, Serfaty, Sylvia, Series editor, Stroppel, Catharina, Series editor, Wienhard, Anna, Series editor, and Kharchenko, Vladislav

Published
2015
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26. Binary Structures

Author

Kharchenko, Vladislav, Morel, J.-M., Editor-in-chief, Teissier, Bernard, Editor-in-chief, De Lellis, Camillo, Series editor, di Bernardo, Mario, Series editor, Figalli, Alessio, Series editor, Khoshnevisan, Davar, Series editor, Kontoyiannis, Ioannis, Series editor, Lugosi, Gabor, Series editor, Podolskij, Mark, Series editor, Serfaty, Sylvia, Series editor, Stroppel, Catharina, Series editor, Wienhard, Anna, Series editor, and Kharchenko, Vladislav

Published
2015
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27. Quantizations of Kac-Moody Algebras

Author

Kharchenko, Vladislav, Morel, J.-M., Editor-in-chief, Teissier, Bernard, Editor-in-chief, De Lellis, Camillo, Series editor, di Bernardo, Mario, Series editor, Figalli, Alessio, Series editor, Khoshnevisan, Davar, Series editor, Kontoyiannis, Ioannis, Series editor, Lugosi, Gabor, Series editor, Podolskij, Mark, Series editor, Serfaty, Sylvia, Series editor, Stroppel, Catharina, Series editor, Wienhard, Anna, Series editor, and Kharchenko, Vladislav

Published
2015
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28. Poincaré-Birkhoff-Witt Basis

Author

Kharchenko, Vladislav, Morel, J.-M., Editor-in-chief, Teissier, Bernard, Editor-in-chief, De Lellis, Camillo, Series editor, di Bernardo, Mario, Series editor, Figalli, Alessio, Series editor, Khoshnevisan, Davar, Series editor, Kontoyiannis, Ioannis, Series editor, Lugosi, Gabor, Series editor, Podolskij, Mark, Series editor, Serfaty, Sylvia, Series editor, Stroppel, Catharina, Series editor, Wienhard, Anna, Series editor, and Kharchenko, Vladislav

Published
2015
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29. Hopf Algebras

Author

Underwood, Robert G., Axler, Sheldon, Series editor, Capasso, Vincenzo, Series editor, Casacuberta, Carles, Series editor, MacIntyre, Angus, Series editor, Ribet, Kenneth, Series editor, Sabbah, Claude, Series editor, Süli, Endre, Series editor, Woyczyński, Wojbor A., Series editor, and Underwood, Robert G.

Published
2015
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30. Applications of Hopf Algebras

Author

Underwood, Robert G., Axler, Sheldon, Series editor, Capasso, Vincenzo, Series editor, Casacuberta, Carles, Series editor, MacIntyre, Angus, Series editor, Ribet, Kenneth, Series editor, Sabbah, Claude, Series editor, Süli, Endre, Series editor, Woyczyński, Wojbor A., Series editor, and Underwood, Robert G.

Published
2015
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31. Covariant Bimodules

Author

Sontz, Stephen Bruce, Axler, Sheldon, Series editor, Capasso, Vincenzo, Series editor, Casacuberta, Carles, Series editor, MacIntyre, Angus, Series editor, Ribet, Kenneth, Series editor, Sabbah, Claude, Series editor, Süli, Endre, Series editor, Woyczyński, Wojbor A., Series editor, and Sontz, Stephen Bruce

Published
2015
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32. First-Order Differential Calculus of a Hopf Algebra

Author

Sontz, Stephen Bruce, Axler, Sheldon, Series editor, Capasso, Vincenzo, Series editor, Casacuberta, Carles, Series editor, MacIntyre, Angus, Series editor, Ribet, Kenneth, Series editor, Sabbah, Claude, Series editor, Süli, Endre, Series editor, Woyczyński, Wojbor A., Series editor, and Sontz, Stephen Bruce

Published
2015
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33. Finite Classical Groups

Author

Sontz, Stephen Bruce, Axler, Sheldon, Series editor, Capasso, Vincenzo, Series editor, Casacuberta, Carles, Series editor, MacIntyre, Angus, Series editor, Ribet, Kenneth, Series editor, Sabbah, Claude, Series editor, Süli, Endre, Series editor, Woyczyński, Wojbor A., Series editor, and Sontz, Stephen Bruce

Published
2015
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34. Introduction

Author

Sontz, Stephen Bruce, Axler, Sheldon, Series editor, Capasso, Vincenzo, Series editor, Casacuberta, Carles, Series editor, MacIntyre, Angus, Series editor, Ribet, Kenneth, Series editor, Sabbah, Claude, Series editor, Süli, Endre, Series editor, Woyczyński, Wojbor A., Series editor, and Sontz, Stephen Bruce

Published
2015
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35. Higher-Order Differential Calculi

Author

Sontz, Stephen Bruce, Axler, Sheldon, Series editor, Capasso, Vincenzo, Series editor, Casacuberta, Carles, Series editor, MacIntyre, Angus, Series editor, Ribet, Kenneth, Series editor, Sabbah, Claude, Series editor, Süli, Endre, Series editor, Woyczyński, Wojbor A., Series editor, and Sontz, Stephen Bruce

Published
2015
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37. Homological algebra for osp(1/2n)

Author

Coulembier, Kevin, Cannarsa, P., editor, Canuto, C., editor, Coletti, G., editor, Marcellini, P., editor, Patrizio, G., editor, Ruggeri, T., editor, Strickland, E., editor, Verra, A., editor, Ancona, V., editor, Gorelik, Maria, editor, and Papi, Paolo, editor

Published
2014
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38. Hopf Algebras

Author

Paugam, Frédéric, Ambrosio, Luigi, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Jost, Jürgen, Series editor, Kollár, János, Series editor, Kudla, Stephen S., Series editor, Laumon, Gérard, Series editor, Lenstra, Hendrik W., Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, and Paugam, Frédéric

Published
2014
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44. Hopf Algebras and Groups

Author

Frédéric Patras and Pierre Cartier

Subjects
Pure mathematics, Mathematics::Quantum Algebra, Mathematics::Rings and Algebras, Algebraic number, Hopf algebra, Mathematics
Abstract

In this chapter, we introduce bialgebras and Hopf algebras, as well as various fundamental related notions and constructions. We discuss briefly their relations to algebraic groups and enveloping algebras that will be detailed later in this book.

Published
2021

45. Combinatorial Hopf Algebras, Twisted Structures, and Species

Author

Frédéric Patras and Pierre Cartier

Subjects
Pure mathematics, Algebraic structure, Countable set, Alphabet, Hopf algebra, Automorphism, Mathematics
Abstract

Various definitions of combinatorial Hopf algebras have been proposed in the literature but no one has been adopted uniformly. Here, we use the name to denote Hopf algebraic structures associated to sets of objects related naturally to a countable alphabet. For example, decorated trees, automorphisms of finite subsets of the alphabet, various families of partitions of these finite subsets, and so on. ”Naturally” refers to the fact that each letter of the alphabet plays the same role and one can exchange them in constructions and formulas.

Published
2021

48. Regev’s Conjecture for Algebras with Hopf Actions

Author

Allan Berele

Subjects
Combinatorics, Sequence, Mathematics::Combinatorics, Conjecture, Zero (complex analysis), Algebra over a field, Hopf algebra, Mathematics
Abstract

Let A be a p.i. algebra in characteristic zero with action from the finite dimensional Hopf algebra H, and let \(\{c_n^H(A)\}\) be the H-codimension sequence. If 1 ∈ A then we prove the H-analogue of Regev’s conjecture, namely, \(c_n^H(A)\simeq \alpha n^t e^n\) for some α > 0, \(2t\in \mathbb {Z}\) and \(e\in \mathbb {N}\). We also prove weaker results under weaker hypotheses.

Published
2020

49. Periods and Superstring Amplitudes

Author

Stephan Stieberger

Subjects
Physics, Riemann hypothesis, symbols.namesake, Pure mathematics, Number theory, Lie algebra, symbols, Superstring theory, Algebraic geometry, Hopf algebra, Complex plane, Moduli space
Abstract

Scattering amplitudes which describe the interaction of physical states play an important role in determining physical observables. In string theory the physical states are given by vibrations of open and closed strings and their interactions are described (at the leading order in perturbation theory) by a world–heet given by the topology of a disk or sphere, respectively. Formally, for scattering of N strings this leads to \(N\!-\!3\)–dimensional iterated real integrals along the compactified real axis or \(N\!-\!3\)–dimensional complex sphere integrals, respectively. As a consequence the physical observables are described by periods on \({\mathscr {M}}_{0,N}\)–the moduli space of Riemann spheres of N ordered marked points. The mathematical structure of these string amplitudes share many recent advances in arithmetic algebraic geometry and number theory like multiple zeta values, single–valued multiple zeta values, Drinfeld, Deligne associators, Hopf algebra and Lie algebra structures related to Grothendiecks Galois theory. We review these results, with emphasis on a beautiful link between generalized hypergeometric functions describing the real iterated integrals on \({\mathscr {M}}_{0,N}(\mathbf{R})\) and the decomposition of motivic multiple zeta values. Furthermore, a relation expressing complex integrals on \({\mathscr {M}}_{0,N}(\mathbf{C})\) as single–valued projection of iterated real integrals on \({\mathscr {M}}_{0,N}(\mathbf{R})\) is exhibited.

Published
2020

50. Perturbative Quantum Field Theory Meets Number Theory

Author

Ivan Todorov

Subjects
Pure mathematics, symbols.namesake, Polylogarithm, Number theory, Subalgebra, Euclidean geometry, symbols, Feynman diagram, Quantum field theory, Hopf algebra, Shuffle algebra, Mathematics
Abstract

Feynman amplitudes are being expressed in terms of a well structured family of special functions and a denumerable set of numbers—periods, studied by algebraic geometers and number theorists. The periods appear as residues of the poles of regularized primitively divergent multidimensional integrals. In low orders of perturbation theory (up to six loops in the massless \(\varphi ^4\) theory) the family of hyperlogarithms and multiple zeta values (MZVs) serves the job. The (formal) hyperlogarithms form a double shuffle differential graded Hopf algebra. Its subalgebra of single valued multiple polylogarithms describes a large class of euclidean Feynman amplitudes. As the grading of the double shuffle algebra of MZVs is only conjectural, mathematicians are introducing an abstract graded Hopf algebra of motivic zeta values whose weight spaces have dimensions majorizing (hopefully equal to) the dimensions of the corresponding spaces of real MZVs. The present expository notes provide an updated version of 2014’s lectures on this subject presented by the author to a mixed audience of mathematicians and theoretical physicists in Sofia and in Madrid.

Published
2020

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