A New Approach to Braided T-Categories and Generalized Quantum Yang–Baxter Equations

We introduce and study a large class of coalgebras (possibly (non)coassociative) with group-algebraic structures Hopf (non)coassociative group-algebras. Hopf (non)coassociative group-algebras provide a unifying framework for classical Hopf algebras and Hopf group-algebras and Hopf coquasigroups. We...

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Bibliographic Details
Published in:Mathematics (Basel) 2022-03, Vol.10 (6), p.968
Main Authors: Zhang, Senlin, Wang, Shuanhong
Format: Article
Language:English
Subjects:
Algebra
braided T-category
Braiding
Hopf (non)coassociative group-algebra
Quantum field theory
quantum Yang–Baxter equation
quasitriangular Hopf (non)coassociative π-algebra
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Summary:We introduce and study a large class of coalgebras (possibly (non)coassociative) with group-algebraic structures Hopf (non)coassociative group-algebras. Hopf (non)coassociative group-algebras provide a unifying framework for classical Hopf algebras and Hopf group-algebras and Hopf coquasigroups. We introduce and discuss the notion of a quasitriangular Hopf (non)coassociative π-algebra and show some of its prominent properties, e.g., antipode S is bijective. As an application of our theory, we construct a new braided T-category and give a new solution to the generalized quantum Yang–Baxter equation.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10060968