Affiliation:
1. Shing-Tung Yau Center, School of Mathematics, Southeast University Nanjing, Jiangsu 210096, People’s Republic of China
Abstract
We introduce and study a large class of algebras (possibly nonassociative) with group-coalgebraic structures, Hopf nonassociative group-coalgebras, which provide a unifying framework for classical Hopf algebras, Turaev’s Hopf group-coalgebras, and Hopf quasigroups. Then, we introduce and discuss the notion of a quasitriangular Hopf π-quasialgebra and show that the category Qrep( H) R of quasirepresentations over any quasitriangular Hopf π-quasialgebra ( H, R) is a braided π-category. As an application of our theory, we give a new solution to the generalized quantum Yang–Baxter equation.
Subject
Mathematical Physics,Statistical and Nonlinear Physics