On stable equivalences of Morita type and nilpotent blocks

TL;DR

This paper provides a new module-theoretic proof that blocks stably equivalent of Morita type to nilpotent blocks are themselves nilpotent, clarifying their structural relationship.

Contribution

It introduces a novel module-theoretic approach to establish the nilpotency of blocks under stable Morita equivalence, building on Puig's prior results.

Findings

Blocks stably equivalent of Morita type to nilpotent blocks are nilpotent

Module-theoretic methods can be used to prove structural properties of blocks

Clarifies the relationship between stable equivalences and nilpotency in block theory

Abstract

In this note, we give a new proof by module-theoretic methods for a result of Puig asserting that blocks which are stable equivalent of Morita type to nilpotent blocks are also nilpotent.