Algebras and Representation Theory

, Volume 18, Issue 5, pp 1267–1297 | Cite as

Automorphisms of the Doubles of Purely Non-Abelian Finite Groups

  • Marc KeilbergEmail author


Using a recent classification of End\((\mathcal {D}(G))\), we determine a number of properties for Aut\((\mathcal {D}(G))\), where \(\mathcal {D}(G)\) is the Drinfel’d double of a finite group G. Furthermore, we completely describe Aut\((\mathcal {D}(G))\) for all purely non-abelian finite groups G. A description of the action of Aut\((\mathcal {D}(G))\) on Rep\((\mathcal {D}(G))\) is also given. We are also able to produce a simple proof that \(\mathcal {D}(G)\cong \mathcal {D}(H)\) if and only if \(\mathcal {G}\cong H\), for G and H finite groups.


Finite groups Automorphisms Endomorphisms Quantum double Tensor autoequivalences 

Mathematics Subject Classification (2010)

16W20 16T05 20D99 


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Faculté des Sciences Mirande, Institut de Mathématiques de BourgogneUniversité de BourgogneDijon CedexFrance

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