Blocks with small-dimensional basic algebra

TL;DR

This paper extends the classification of p-blocks of finite groups with basic algebra dimensions of 13 and 14, confirming the finiteness of Morita equivalence classes as predicted by Donovan's Conjecture.

Contribution

It advances the classification of blocks with small-dimensional basic algebras from dimension 12 to 14, supporting Donovan's Conjecture.

Findings

Finitely many Morita equivalence classes for dimensions 13 and 14

Extension of previous classification up to dimension 12

Confirmation of Donovan's Conjecture predictions

Abstract

Linckelmann and Murphy have classified the Morita equivalence classes of p-blocks of finite groups whose basic algebra has dimension at most 12. We extend their classification to dimension 13 and 14. As predicted by Donovan's Conjecture, we obtain only finitely many such Morita equivalence classes.