Blocks of group algebras are derived simple

TL;DR

This paper proves that blocks of group algebras of finite groups have simple derived categories, meaning they cannot be decomposed further, regardless of the field's characteristic.

Contribution

It establishes a derived analogue of Maschke's theorem, showing the derived categories of all blocks are simple and indecomposable.

Findings

Derived categories of blocks are simple and admit no nontrivial recollements.

The result holds independently of the characteristic of the base field.

Provides a new understanding of the structure of block algebras in representation theory.

Abstract

A derived version of Maschke's theorem for finite groups is proved: the derived categories, bounded or unbounded, of all blocks of the group algebra of a finite group are simple, in the sense that they admit no nontrivial recollements. This result is independent of the characteristic of the base field.