Morita equivalence classes of 2-blocks of defect three

TL;DR

This paper classifies Morita equivalence classes of certain blocks with elementary abelian defect groups of order 8, verifies Broué's conjecture for these blocks, and completes the classification for blocks of defect at most three.

Contribution

It provides a complete description of Morita and derived equivalence classes for blocks with elementary abelian defect groups of order 8 and confirms Broué's conjecture for these cases.

Findings

Verification of Broué's abelian defect group conjecture for these blocks

Complete classification of Morita and derived equivalence classes for blocks of defect at most three

Description of derived equivalences between these blocks

Abstract

We give a complete description of the Morita equivalence classes of blocks with elementary abelian defect groups of order 8 and of the derived equivalences between them. A consequence is the verification of Brou\'e's abelian defect group conjecture for these blocks. It also completes the classification of Morita and derived equivalence classes of 2-blocks of defect at most three defined over a suitable field.