For self-injective algebras, Rickard proved that each derived equivalence induces a stable
equivalence of Morita type. For general algebras, it is unknown when a derived equivalence …

We consider the question of lifting stable equivalences of Morita type to derived
equivalences. One motivation comes from an approach to Broué's abelian defect group …

In the representation theory of finite groups, there is a well-known and important conjecture
due to M. Broué. He conjectures that, for any prime p, if a p-block A of a finite group G has an …

Derived categories and equivalences between them are the pièce de résistance of modern
homological algebra. They are widely used in many branches of mathematics, especially in …

We define a block-reduced version of the crystal graph of spin representations of the
symmetric and alternating groups, and separate it into layers, each obtained by translating …

In representation theory of finite groups, there is a well-known and important conjecture due
to M. Broué. He conjectures that, for any prime p, if a p-block A of a finite group G has an …

We investigate the simple modules for the sporadic simple Mathieu groups M22, M23 and
M24 as well as those of the automorphism group, the covering groups and the bicyclic …

Let B be a p-block of a finite group G with abelian defect group D such that S≤ G≤ Aut (S),
S′= S and S/Z (S) is a sporadic simple group. We show that B is isotypic to its Brauer …

In the representation theory of finite groups, Broué's abelian defect group conjecture says
that for any prime p, if a p-block A of a finite group G has an abelian defect group P, then A …

Similarities between the character tables of a block with abelian defect group and of its
Brauer correspondent have been observed long time ago. This led in the late 1980's to the …