Blocks with normal Abelian defect and Abelian p' inertial quotient

David Benson, Radha Kessar, Markus Linckelmann

Research output: Contribution to journalArticlepeer-review

Abstract

Let k be an algebraically closed field of characteristic p⁠, and let O be either k or its ring of Witt vectors W(k)⁠. Let G be a finite group and B a block of OG with normal abelian defect group and abelian p′ inertial quotient L⁠. We show that B is isomorphic to its second Frobenius twist. This is motivated by the fact that bounding Frobenius numbers is one of the key steps towards Donovan’s conjecture. For O=k⁠, we give an explicit description of the basic algebra of B as a quiver with relations. It is a quantized version of the group algebra of the semidirect product P⋊L⁠.
Original languageEnglish
Pages (from-to)1437-1448
Number of pages12
JournalQ. J. Math.
Volume70
Issue number4
DOIs
Publication statusPublished - 21 Oct 2019

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