Broué's Conjecture Holds for Principal 3-Blocks with Elementary Abelian Defect Group of Order 9☆
By Shigeo Koshitani, Naoko Kunugi. 2002
55 citations recorded by the source corpus.
Abstract In representation theory of finite groups, there is a well-known and important conjecture due to M. Broue. He conjectures that, for any prime p, if a finite group G has an abelian Sylow p-subgroup P, then the derived categories of the principal p-blocks of G and of the normalizer NG(P) of P in G are equivalent. We prove in this paper that Broue'Inage-kus conjecture holds for the principal 3-block of an arbitrary finite group G with an elementary abelian Sylow 3-subgroup P of order 9, by using initiated works for the case where G is simple, which are due to Puig, Okuyama, Waki, Miyachi, and the authors. The result depends on the classification of finite simple groups.
Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/49b202e684054b4a663a246a2477febf43089122
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Citations in the corpus
- Perverse equivalences and Brouéʼs conjecture (2010, background): “The case = 3 of (a) is due to Koshitani and Kunugi [28], while the case = 2 is due to Marcus [38].”
- Block theory via stable and Rickard equivalences (2001, unknown): “The conjecture holds for • D cyclic [Ri1, Li1, Rou2] andD Z/2×Z/2 ([Ri4, Li2, Li3, Rou3] and §6.3 for principal blocks) • G p-solvable [Da1, Pu1, HaLi] • G a connected reductive algebraic group overFq andp dividesq−1 butp does not divide the order of the Weyl group [Pu2] • G a symmetric group andD Z”