The primitive idempotents of the p-permutation ring

TL;DR

This paper provides explicit formulas for primitive idempotents in the p-permutation ring of a finite group over fields of characteristic 0 and p, aiding the understanding of its algebraic structure.

Contribution

It introduces explicit formulae for primitive idempotents in the p-permutation ring, enhancing the algebraic understanding of p-permutation modules.

Findings

Explicit formulas for primitive idempotents derived

Clarifies structure of p-permutation ring

Facilitates computations in modular representation theory

Abstract

Let G be a finite group, let p be a prime number, and let K be a field of characteristic 0 and k be a field of characteristic p, both large enough. In this note we state explicit formulae for the primitive idempotents of K\otimes pp_k(G), where pp_k(G) is the ring of p-permutation kG-modules.