Abstract
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.
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31 January 2019
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Presented by Susan Montgomery.
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Keilberg, M. Automorphisms of the Doubles of Purely Non-Abelian Finite Groups. Algebr Represent Theor 18, 1267–1297 (2015). https://doi.org/10.1007/s10468-015-9540-0
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DOI: https://doi.org/10.1007/s10468-015-9540-0