On stable equivalences with endopermutation source and K\"ulshammer--Puig classes

TL;DR

This paper provides a new proof demonstrating that stable equivalences of Morita type, induced by bimodules with endopermutation sources, preserve K"ulshammer--Puig classes in block algebras of finite groups.

Contribution

It offers a novel proof using existing notation to show the preservation of K"ulshammer--Puig classes under certain stable equivalences, extending Puig's result.

Findings

Stable equivalences of Morita type preserve K"ulshammer--Puig classes.

The proof uses the notation and framework from Lin18b.

The result applies to block algebras of finite groups with endopermutation sources.

Abstract

We give a new proof, by using the terminology and notation in the textbook \cite{Lin18b}, to a result, due to Puig, stating that a stable equivalence of Morita type between two block algebras of finite groups induced by a bimodule with an endopermutation source preserves K\"ulshammer--Puig classes.