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
This article is devoted to the study of the symmetry in the Yetter-Drinfeld category of a finite-dimensional weak Hopf algebra.It generalizes the corresponding results in Hopf algebras.
For a path algebra A = kQ with Q an arbitrary quiver, consider the Hochschild homology groups Hn(A) and the homology groups TornAe(A, A), where Ae is the enveloping algebra of A. In this paper the groups are explicitly given.
This is a note on Abrams＇ paper ＂Modules, Comodules, and Cotensor Products over Frobenius Algebras, Journal of Algebras＂ （1999）. With the application of Frobenius coordinates developed recently by Kadison, one has a direct proof of Abrams＇ characterization for Frobenius algebras in terms of comultiplication （see L. Kadison （1999））. For any Frobenius algebra, by using the explicit comultiplication, the explicit correspondence between the category of modules and the category of comodules is obtained. Moreover, with this we give very simplified proofs and improve Abrams＇ results on the Hom functor description of cotensor functor.
