Basic Morita equivalences and a conjecture of Sasaki for cohomology of block algebras of finite groups

TL;DR

This paper proves Sasaki's conjecture for a new class of blocks called nilpotent covered blocks using basic Morita equivalences, and explores transfer maps in cohomology and Hochschild cohomology.

Contribution

It establishes Sasaki's conjecture for nilpotent covered blocks via Morita equivalences and analyzes associated transfer maps in cohomology.

Findings

Sasaki's conjecture holds for nilpotent covered blocks

Transfer maps between cohomology and Hochschild cohomology are constructed and analyzed

Morita equivalences are used to relate block algebras in the proof

Abstract

We show, using basic Morita equivalences between block algebras of finite groups, that the Conjecture of H. Sasaki from [9] is true for a new class of blocks called nilpotent covered blocks. When this Conjecture is true we define some transfer maps between cohomology of block algebras and we analyze them through transfer maps between Hochschild cohomol- ogy algebras.