Representations of Nonstandard Poincaré Hopf Algebras

Abstract

Let 𝔭 _q (1 + 1) be a nonstandard Poincaré Hopf algebra, we characterize all finite dimensional completely E-semisimple modules of 𝔭 _q (1 + 1). We also classify all finite dimensional E-semisimple modules of 𝔭 _q for a special quotient algebra of 𝔭 _q (1 + 1). Moreover, the decomposition of tensor product of two finite dimensional E-semisimple indecomposable modules is obtained.

Key Words:

• Completely semisimple
• Hopf algebra
• Representation

2000 Mathematics Subject Classification:

• Primary 16W30
• Secondary 17B37

ACKNOWLEDGMENTS

The first author is supported by NSFC (Grant 10671016) and NSF of Beijing (Grant 1062003), and the second author acknowledges the support of DAAD. This work was done when the first author visited Stuttgart University, Germany. He is very grateful to Prof. Dipper for the hospitality during the stay.

Notes

Communicated by R. Wisbauer.