β-character Algebra and a Commuting Pair in Hopf Algebras |
| |
Authors: | Jun Hu Yinhuo Zhang |
| |
Affiliation: | (1) Department of Applied Mathematics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China;(2) School of Mathematics, Statistics and Computer Science, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand |
| |
Abstract: | Let K be a field. Let H be a finite-dimensional semisimple and cosemisimple K-Hopf algebra. In this paper, we introduce a notion of β-character algebra C β (H) for each group-like element β in H ∗. We prove that Radford’s action of the Drinfel’d double D(H) on H β (see Radford, J. Algebra, 270:670–695, 2003) and the right hit action of the β-character algebra C β (H) on H β form a commuting pair. This generalizes an earlier result of Zhu (Proc. Amer. Math. Soc., 125(10):2847–2851, 1997). A K-basis of C β (H) is given when H is split semisimple. Finally, as an example, we explicitly construct all the simple modules for the Drinfel’d double of the unique 8-dimensional non-commutative and non-cocommutative semisimple Hopf algebra. Presented by S. Montgomery. |
| |
Keywords: | Hopf algebra Character algebra Drinfel’ d double |
本文献已被 SpringerLink 等数据库收录! |
|