On blocks stably equivalent to a quantum complete intersection
of dimension 9 in characteristic 3 and a case of the abelian
defect group conjecture

Radha Kessar

Abstract. Using a stable equivalence due to Rouquier, we prove
that Brou\'e's abelian defect group conjecture holds for 3-blocks
of defect 2 whose Brauer correspondent has a unique isomorphism
class of simple modules. The proof makes use of the fact, also 
due to Rouquier, that a stable equivalence of Morita type between
self-injecture algebras induces an isomorphism between the 
connected components of the outer automorphism groups of the 
algebras.