Derived Picard groups of selfinjective Nakayama algebras

TL;DR

This paper completes the calculation of the derived Picard group for selfinjective Nakayama algebras, building on previous work and new techniques involving orbit categories.

Contribution

It provides a full determination of the derived Picard group for these algebras, extending earlier partial results and methods.

Findings

Complete computation of the derived Picard group for selfinjective Nakayama algebras.

Utilized orbit category techniques to finalize the group structure.

Extended previous results for Brauer tree algebras to Nakayama algebras.

Abstract

In our proceeding paper a generating set of the derived Picard group of a selfinjective Nakayama algebra was constructed combining some previous results for Brauer tree algebras and the technique of orbit categories developed there. In this paper we finish the computation of the derived Picard group of a selfinjective Nakayama algebra.