Results 1 to 10 of about 29,381 (154)
Combinatorial Hopf Algebras and Towers of Algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras $\bigoplus_{n \geq 0}A_n$ can be endowed with the structure of graded dual Hopf algebras.
Nantel Bergeron, Thomas Lam, Huilan Li
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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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A New Approach to Braided T-Categories and Generalized Quantum Yang–Baxter Equations
Mathematics, 2022 We introduce and study a large class of coalgebras (possibly (non)coassociative) with group-algebraic structures Hopf (non)coassociative group-algebras.
Senlin Zhang, Shuanhong Wang
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Combinatorial Hopf Algebras of Simplicial Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We consider a Hopf algebra of simplicial complexes and provide a cancellation-free formula for its antipode. We then obtain a family of combinatorial Hopf algebras by defining a family of characters on this Hopf algebra.
Carolina Benedetti +2 more
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Lattice of combinatorial Hopf algebras: binary trees with multiplicities [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 In a first part, we formalize the construction of combinatorial Hopf algebras from plactic-like monoids using polynomial realizations. Thank to this construction we reveal a lattice structure on those combinatorial Hopf algebras.
Jean-Baptiste Priez
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Rota–Baxter (Co)algebra Equation Systems and Rota–Baxter Hopf Algebras
Mathematics, 2022 We introduce and discuss the notions of Rota–Baxter bialgebra equation systems and Rota–Baxter Hopf algebras. Then we construct a lot of examples based on Hopf quasigroups.
Yue Gu, Shuanhong Wang, Tianshui Ma
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Boundary and domain wall theories of 2d generalized quantum double model
Journal of High Energy Physics, 2023 The generalized quantum double lattice realization of 2d topological orders based on Hopf algebras is discussed in this work. Both left-module and right-module constructions are investigated.
Zhian Jia +2 more
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Generalized Hopf–Ore Extensions of Hopf Group-Coalgebras
Mathematics, 2022 In this paper, we introduce the concept of a generalized Hopf–Ore extension of a Hopf group-coalgebra and give the necessary and sufficient conditions for the Ore extension of a Hopf group-coalgebra to be a Hopf group-coalgebra.
Ding-Guo Wang, Xing Wang
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A Hopf algebra of subword complexes (Extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We introduce a Hopf algebra structure of subword complexes, including both finite and infinite types. We present an explicit cancellation free formula for the antipode using acyclic orientations of certain graphs, and show that this Hopf algebra induces ...
Nantel Bergeron, Cesar Ceballos
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Partial categorification of Hopf algebras and representation theory of towers of \mathcalJ-trivial monoids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 This paper considers the representation theory of towers of algebras of $\mathcal{J} -trivial$ monoids. Using a very general lemma on induction, we derive a combinatorial description of the algebra and coalgebra structure on the Grothendieck rings $G_0 ...
Aladin Virmaux
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