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

Senlin Zhang and Shuanhong Wang
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Senlin Zhang: School of Mathematics, Southeast University, Nanjing 210096, China
Shuanhong Wang: Shing-Tung Yau Center, School of Mathematics, Southeast University, Nanjing 210096, China

Mathematics, 2022, vol. 10, issue 6, 1-40

Abstract: 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.

Keywords: braided T-category; quantum Yang–Baxter equation; Hopf (non)coassociative group-algebra; quasitriangular Hopf (non)coassociative ? -algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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