Forum of Mathematics, Sigma (Jan 2023)
Structure of blocks with normal defect and abelian $p'$ inertial quotient
Abstract
Let k be an algebraically closed field of prime characteristic p. Let $kGe$ be a block of a group algebra of a finite group G, with normal defect group P and abelian $p'$ inertial quotient L. Then we show that $kGe$ is a matrix algebra over a quantised version of the group algebra of a semidirect product of P with a certain subgroup of L. To do this, we first examine the associated graded algebra, using a Jennings–Quillen style theorem.
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