The extension algebra of some cohomological Mackey functors

TL;DR

This paper introduces a new inflation functor for cohomological Mackey functors over finite groups and provides an explicit algebraic description of self-extensions for simple functors in specific cases.

Contribution

It develops a novel inflation functor and uses it to explicitly describe the extension algebra of simple cohomological Mackey functors for certain groups.

Findings

Constructed a new inflation functor for cohomological Mackey functors.

Provided an explicit presentation of the extension algebra for elementary abelian p-groups.

Focused on cases where p is odd and G is an elementary abelian p-group.

Abstract

Let $k$ be a field of characteristic $p$. We construct a new inflation functor for cohomological Mackey functors for finite groups over $k$. Using this inflation functor, we give an explicit presentation of the graded algebra of self extensions of the simple functor $S_\un^G$, when $p$ is odd and $G$ is an elementary abelian $p$-group.