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Cartan matrices and Brauer's k(B)-Conjecture V

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arxiv 1911.10710 v1 pith:H3GWCUPG submitted 2019-11-25 math.RT

Cesare G. Ardito , Benjamin Sambale This is my paper · ORCID
classification math.RT
keywords blocksdefectbrauerconjectureabelianactionalgorithmbasic
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We prove Brauer's k(B)-Conjecture for the 3-blocks with abelian defect groups of rank at most 5 and for all 3-blocks of defect at most 4. For this purpose we develop a computer algorithm to construct isotypies based on a method of Usami and Puig. This leads further to some previously unknown perfect isometries for the 5-blocks of defect 2. We also investigate basic sets which are compatible under the action of the inertial group.

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  1. Morita equivalence classes of blocks with elementary abelian defect groups of order 32

    math.RT 2019-08 conditional novelty 7.0 of 10

    Blocks with elementary abelian defect group (C2)^5 are shown to be Morita equivalent to exactly one of 34 listed block algebras, and Harada's conjecture is verified for them.

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