The group of splendid morita equivalences of principal 2-blocks with dihedral and generalised quaternion defect groups
buir.contributor.author | Karagüzel, Çisil | |
buir.contributor.author | Yılmaz, Deniz | |
buir.contributor.orcid | Karagüzel, Çisil|0000-0002-1129-3510 | |
buir.contributor.orcid | Yılmaz, Deniz|0000-0002-4245-8154 | |
dc.citation.epage | 167 | |
dc.citation.spage | 160 | |
dc.citation.volumeNumber | 35 | |
dc.contributor.author | Karagüzel, Çisil | |
dc.contributor.author | Yılmaz, Deniz | |
dc.date.accessioned | 2025-02-27T08:14:01Z | |
dc.date.available | 2025-02-27T08:14:01Z | |
dc.date.issued | 2024-01-09 | |
dc.department | Department of Mathematics | |
dc.description.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 $\calT(B)$ 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.doi | 10.24330/ieja.1402947 | |
dc.identifier.eissn | 1306-6048 | |
dc.identifier.uri | https://hdl.handle.net/11693/116910 | |
dc.language.iso | English | |
dc.publisher | International Electronic Journal of Algebra | |
dc.relation.isversionof | https://doi.org/10.24330/ieja.1402947 | |
dc.source.title | International Electronic Journal of Algebra | |
dc.subject | Block | |
dc.subject | Fusion system | |
dc.subject | Picard group | |
dc.subject | Dihedral defect group | |
dc.subject | Generalised quaternion defect group | |
dc.title | The group of splendid morita equivalences of principal 2-blocks with dihedral and generalised quaternion defect groups | |
dc.type | Article |
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