Stable Green ring of the Drinfeld doubles of the generalised Taft algebras (corrections and new results)

TL;DR

This paper revisits the fusion rules for the Drinfeld double of duals of generalized Taft algebras, correcting previous errors and providing new results on module classifications and fusion rules.

Contribution

It corrects earlier proofs using stable homomorphisms and introduces new fusion rule results and classifications of endotrivial and algebraic modules.

Findings

Corrected previous proofs with stable homomorphisms

Completed fusion rule classifications for previously unstudied modules

Provided new classifications of endotrivial and algebraic modules

Abstract

We return to the fusion rules for the Drinfeld double of the duals of the generalised Taft algebras that we studied in [9]. We first correct some proofs and statements in [9] that were incorrect, using stable homomorphisms. We then complete this with new results on fusion rules for the modules we had not studied in [9] and a classification of endotrivial and algebraic modules.