Bockstein homomorphisms for Hochschild cohomology of group algebras and of block algebras of finite groups

TL;DR

This paper provides explicit constructions and properties of Bockstein homomorphisms in Hochschild cohomology for group and block algebras, utilizing additive decompositions and product formulas.

Contribution

It introduces explicit definitions of Bockstein homomorphisms for Hochschild cohomology of group and block algebras, extending existing formulas and decompositions.

Findings

Established additive decomposition for cohomology algebra of defect groups

Derived product formula for Hochschild cohomology of block algebras

Defined Bockstein homomorphisms for source algebras in blocks

Abstract

We give an explicit approach for Bockstein homomorphisms of the Hochschild cohomology of a group algebra and of a block algebra of a finite group and we show some properties. To give explicit definitions for these maps we use an additive decomposition and a Product Formula for the Hochschild cohomology of group algebras given by Siegel and Witherspoon in 1999. For k an algebraically closed field of characteristic p and G a finite group we prove an additive decomposition and a Product Formula for the cohomology algebra of a defect group of a block ideal of kG with coefficients in the source algebra of this block, and we define similar Bockstein homomorphisms.