The group of splendid Morita equivalences of principal 2-blocks with dihedral and generalised quaternion defect groups

2023/06/13 by Çısıl Karagüzel, Deniz Yılmaz, Karagüzel, Çisil +1
Mathematics · #Finite Group Theory Research #Advanced Algebra and Geometry #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2306.07708

Abstract

Let k be an algebraically closed field of characteristic 2, let G be a finite group and let B be the principal 2-block of kG with a dihedral or a generalised quaternion defect group P. Let also T(B) denote the group of splendid Morita auto-equivalences of B. We show that T(B)≅ Out_P(A)\rtimes Out(P,F) , where Out(P,F) is the group of outer automorphisms of P which stabilize the fusion system F of G on P and Out_P(A) is the group of algebra automorphisms of a source algebra A of B fixing P modulo inner automorphisms induced by (A^P)^×.

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