About the site

This wiki site grew out of EPSRC grant EP/M015548/1 Morita equivalence classes of blocks, which had the primary purpose of applying the classification of finite simple groups to Donovan's conjecture and to the classification of blocks of finite groups up to Morita equivalence.

Blocks with cyclic defect groups are well understood, and the theory of tame blocks is very advanced, although even in these cases the classification of blocks is not fully understood. Some wild cases are understood because the defect group forces the block to be nilpotent, using fusion arguments. In the remaining cases the classification of finite simple groups is required.

The purpose of this site is to:

• keep a record of progress on the major conjectures in the area
• record the classification of Morita equivalences as it progresses
• record Morita invariants of blocks
• provide background material in order to understand the above.

One Morita invariant that has become increasingly important in classification results is the Picard group. Part of the site is dedicated to these.

The site is maintained at the University of Manchester. It was set up by Charles Eaton with the valuable help of Cesare Ardito and Bob Nutter