Tensor Products of Modules Over a Certain Class of Quantum Doubles

Abstract

The quantum doubles of a certain class of rank two pointed Hopf algebras are considered. The socle of the tensor product of two such modules is computed, and formulas similar to the ones in [4] are obtained. Cases when such a tensor product is completely irreducible are also given in the last section.

Key Words:

• Pointed Hopf algebras
• Quantum doubles
• Tensor product

2000 Mathematics Subject Classification:

• Primary 16W30
• Secondary 16W35, 20G42

ACKNOWLEDGMENT

Research partially supported by PN-II-RU-PD-2009 CNCSIS grant PD-168, No. 14/28.07.2010.

Notes

Communicated by J. Zhang.