Trace-Like Invariant for Representations of Nilpotent Liftings of Quantum Planes

Abstract

We derive a formula for the trace of the antipode on endomorphism algebras of simple self-dual modules of nilpotent liftings of quantum planes. We show that the trace is equal to the quantum dimension of the module up to a nonzero scalar depending on the simple module.

Key Words:

• Hopf algebras
• Liftings of quantum planes
• Trace of the antipode

2000 Mathematics Subject Classification:

• 16W30
• 16G99

Notes

Communicated by M. Cohen.