Results 31 to 40 of about 297 (183)
Hopf algebras and the logarithm of the S-transform in free probability ― Extended abstract [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 This document is an extended abstract of the paper `Hopf algebras and the logarithm of the S-transform in free probability' in which we introduce a Hopf algebraic approach to the study of the operation $\boxtimes$ (free multiplicative convolution) from ...
Mitja Mastnak, Alexandru Nica
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Hopf algebras with triality [PDF]
Transactions of the American Mathematical Society, 2012 In this paper we revisit and extend the constructions of Glauberman and Doro on groups with triality and Moufang loops to Hopf algebras. We prove that the universal enveloping algebra of any Lie algebra with triality is a Hopf algebra with triality. This allows us to give a new construction of the universal enveloping algebras of Malcev algebras.
Benkart, Georgia +2 more
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MathematicsIn this paper, we introduce and study the notion of a multiplier left Hopf algebra, which can be seen as an extension of the Van Daele’s multiplier Hopf algebras and the Green–Nichols–Taft’s left Hopf algebras.
Chunxiao Yan, Shuanhong Wang
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3-dimensional Λ-BMS symmetry and its deformations
Journal of High Energy Physics, 2021 In this paper we study quantum group deformations of the infinite dimensional symmetry algebra of asymptotically AdS spacetimes in three dimensions. Building on previous results in the finite dimensional subalgebras we classify all possible Lie bialgebra
Andrzej Borowiec +2 more
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A Hopf module characterization of Hopf algebras [PDF]
Proceedings of the American Mathematical Society, 1983 A bialgebra over a field is a Hopf algebra if and only if all (nonzero) right Hopf modules are free, as modules, on a set of invariants.
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Frobenius–Schur Indicator for Categories with Duality
Axioms, 2012 We introduce the Frobenius–Schur indicator for categories with duality to give a category-theoretical understanding of various generalizations of the Frobenius–Schur theorem including that for semisimple quasi-Hopf algebras, weak Hopf C*-algebras and ...
Kenichi Shimizu
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On indicators of Hopf algebras [PDF]
Israel Journal of Mathematics, 2015 Kashina, Montgomery and Ng introduced the $n$-th indicator $ν_n(H)$ of a finite-dimensional Hopf algebra $H$ and showed that the indicators have some interesting properties such as the gauge invariance. The aim of this paper is to investigate the properties of $ν_n$'s. In particular, we obtain the cyclotomic integrality of $ν_n$ and a formula for $ν_n$
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Ore Extensions of Multiplier Hopf Coquasigroups
AxiomsThis paper introduces and investigates Ore extensions in the context of multiplier Hopf coquasigroups, a structure that generalizes both multiplier Hopf algebras and Hopf coquasigroups.
Rui Zhang +3 more
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Algebraic and combinatorial structures on Baxter permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We give a new construction of a Hopf subalgebra of the Hopf algebra of Free quasi-symmetric functions whose bases are indexed by objects belonging to the Baxter combinatorial family (\emphi.e.
Samuele Giraudo
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Journal of Algebra, 2004 If \(Q\) is a Schurian Hopf quiver and \(k\) is a field of characteristic zero, the simple pointed Hopf subalgebras of a graded Hopf algebra structure on the path coalgebra \(kQ^c\) are classified. A dual Gabriel theorem for pointed Hopf algebras is proved.
Van Oystaeyen, Fred, Zhang, Pu
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