The Second Indicator and the Trace of the Antipode for Representations of a Class of Hopf Algebras of Andruskiewitch-Schneider Type

Abstract

We give definition of the second indicator for any finite-dimensional Hopf algebra over an algebraically closed field of characteristic 0 with the square of antipode an inner automorphism. We derive a closed formula for the trace of the antipode on endomorphism algebras of simple self-dual modules of nilpotent type liftings of quantum linear spaces and compute the value of their second indicators. Uniqueness of indicators is examined.

Key Words:

• Hopf algebras
• Liftings of quantum linear spaces
• The second Frobenius–Schur indicator
• Trace of the antipode

2000 Mathematics Subject Classification:

• 16W30
• 16G99

Notes

Communicated by S. Montgomery.

To Mia Cohen in honor of her contributions to mathematics.