Character triples and equivalences over a group graded G-algebra

TL;DR

This paper introduces Morita and Rickard equivalences for group graded G-algebras, showing they preserve certain character relations and extend block equivalences in modular representation theory.

Contribution

It develops new Morita and Rickard equivalences for group graded G-algebras, linking block extensions and character triples.

Findings

Morita and Rickard equivalences over G-algebras are established.

These equivalences imply Späth's central order relation between character triples.

The work extends the understanding of block extensions in modular representation theory.

Abstract

We introduce Morita and Rickard equivalences over a group graded G-algebra between block extensions. A consequence of such equivalences is that Sp\"ath's central order relation holds between two corresponding character triples.