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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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Duality theory of $p$-adic Hopf algebras [PDF]
Categories and General Algebraic Structures with Applications, 2021 We show the monoidal functoriality of Schikhof duality, and cultivate new duality theory of $p$-adic Hopf algebras. Through the duality, we introduce two sorts of $p$-adic Pontryagin dualities.
Tomoki Mihara
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Primitive Cohomology of Hopf algebras [PDF]
, 2015 Primitive cohomology of a Hopf algebra is defined by using a modification of the cobar construction of the underlying coalgebra. Among many of its applications, two classifications are presented.
Wang, D. -G., Zhang, J. J., Zhuang, G.
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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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Monoidal Hom-Hopf algebras [PDF]
, 2013 Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal category such ...
A. Makhlouf +10 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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Generalized Hopf-Ore extensions
, 2018 We derive necessary and sufficient conditions for an Ore extension of a Hopf algebra to have a Hopf algebra structure of a certain type. This construction generalizes the notion of Hopf-Ore extension, called a generalized Hopf-Ore extension.
Chen, Huixiang, Wang, Zhen, You, Lan
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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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Kernels of representations and coideal subalgebras of Hopf algebras
, 2010 We define left and right kernels of representations of Hopf algebras. In the case of group algebras, left and right kernels coincide and they are the usual kernels of modules.
Andruskiewitsch +7 more
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