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

buir.contributor.authorKaragüzel, Çisil
buir.contributor.authorYılmaz, Deniz
buir.contributor.orcidKaragüzel, Çisil|0000-0002-1129-3510
buir.contributor.orcidYılmaz, Deniz|0000-0002-4245-8154
dc.citation.epage167
dc.citation.spage160
dc.citation.volumeNumber35
dc.contributor.authorKaragüzel, Çisil
dc.contributor.authorYılmaz, Deniz
dc.date.accessioned2025-02-27T08:14:01Z
dc.date.available2025-02-27T08:14:01Z
dc.date.issued2024-01-09
dc.departmentDepartment of Mathematics
dc.description.abstractLet $k$ 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 $\calT(B)$ denote the group of splendid Morita auto-equivalences of $B$. We show that $$\begin{align*} \calT(B)\cong \Out_P(A)\rtimes \Out(P,\calF), \end{align*}$$ where $\Out(P,\calF)$ is the group of outer automorphisms of $P$ which stabilize the fusion system $\calF$ 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 ($A^P)^\times$.
dc.identifier.doi10.24330/ieja.1402947
dc.identifier.eissn1306-6048
dc.identifier.urihttps://hdl.handle.net/11693/116910
dc.language.isoEnglish
dc.publisherInternational Electronic Journal of Algebra
dc.relation.isversionofhttps://doi.org/10.24330/ieja.1402947
dc.source.titleInternational Electronic Journal of Algebra
dc.subjectBlock
dc.subjectFusion system
dc.subjectPicard group
dc.subjectDihedral defect group
dc.subjectGeneralised quaternion defect group
dc.titleThe group of splendid morita equivalences of principal 2-blocks with dihedral and generalised quaternion defect groups
dc.typeArticle

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