Automorphisms of the doubles of purely non-abelian finite groups

2013/11/04 by Marc Keilberg, Keilberg, Marc
Mathematics · #16T05 #16W20 #20D99 #FOS: Mathematics #Group Theory (math.GR) #Quantum Algebra (math.QA) #math.GR #math.QA #msc:16T05 #msc:16W20 #msc:20D99

paper · pdf · doi:10.48550/arxiv.1311.0575

39 pages; title changed; results expanded; notation and proofs substantially improved; a few corrections (proof that u was always Hopf was flawed, and has been removed)

arxiv created 2014/06/08 · arxiv updated 2014/06/10

Abstract

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

Related

• Finite Groups with Abelian Automorphism Groups: A Survey
• Automorphisms of finite Abelian groups
• On the automorphisms of the Drinfel'd double of a Borel Lie subalgebra
• Automorphisms of Finite Abelian Groups
• Actions of Drinfeld doubles of finite groups on Artin-Schelter regular algebras