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

Article, Preprint English OPEN
Kessar, Radha (2010)
  • Publisher: Cambridge University Press
  • Related identifiers: doi: 10.1112/jlms/jdr047
  • Subject: QA | 20C20, 16D90 | Mathematics - Group Theory | Mathematics - Representation Theory
    arxiv: Mathematics::Representation Theory

Using a stable equivalence due to Rouquier, we prove that Broue'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-injective algebras induces an isomorphism between the connected components of the outer automorphism groups of the algebras.
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