Morita equivalence classes of principal blocks with elementary abelian defect groups of order 64

TL;DR

This paper classifies the Morita equivalence classes of principal blocks with elementary abelian defect groups of order 64 over a complete discrete valuation ring with an algebraically closed residue field of characteristic two.

Contribution

It provides a complete classification of Morita equivalence classes for these blocks, advancing understanding in modular representation theory.

Findings

Complete classification of Morita equivalence classes for the specified blocks.

Identification of invariants distinguishing different classes.

Extension of known results to larger elementary abelian defect groups.

Abstract

We classify the Morita equivalence classes of principal blocks with elementary abelian defect groups of order 64 with respect to a complete discrete valuation ring with an algebraically closed residue field of characteristic two.