Using the quiver technique we construct a class of non-graded bi-Frobenius algebras. We also classify a class of graded bi-Frobenius algebras via certain equations of structure coefficients.
Yan-hua WANG & Xiao-wu CHEN Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China
In this paper,a super version of the Hopf quiver theory is developed.The notion of Hopf superquivers is introduced.It is shown that only the path supercoalgebras of Hopf superquivers admit graded Hopf superalgebra structures.A complete classification of such graded Hopf superalgebras is given.A superquiver setting for general pointed Hopf superalgebras is also built up.In particular,a super version of the Gabriel type theorem and the Cartier-Gabriel decomposition theorem is given.
This is a contribution to the project of quiver approaches to quasi-quantum groups.We classify Majid bimodules over groups with 3-cocycles by virtue of projective representations.This leads to a theoretic classification of graded pointed Majid algebras over path coalgebras,or equivalently cofree pointed coalgebras,and helps to provide a projective representation-theoretic description of the gauge equivalence of graded pointed Majid algebras.We apply this machinery to construct some concrete examples and obtain a classification of finite-dimensional graded pointed Majid algebras with the set of group-likes equal to the cyclic group of order 2.
