Quantum double of a (locally) compact group

1996/05/29 by T. H. Koornwinder, Koornwinder, T. H., N. M. Muller +1
Mathematics · Physics and Astronomy · #22D20 #22D30 (Primary) #81R50 (secondary) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.QA #msc:22D20 #msc:22D30 #msc:81R50 #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9605044

LaTeX2e, 18 pages. Univ. of Amsterdam, Depts. of Math. and of Theor.Phys., to be published in the Journal of Lie Theory

arxiv created 1996/10/02 · arxiv updated 2009/11/30

Abstract

We generalise the quantum double construction of Drinfel'd to the case of the (Hopf) algebra of suitable functions on a compact or locally compact group. We will concentrate on the *-algebra structure of the quantum double. If the conjugacy classes in the group are countably separated, then we classify the irreducible *-representations by using the connection with so-called transformation group algebras. For finite groups, we will compare our description to the result of Dijkgraaf, Pasquier and Roche. Finally we will work out the explicit examples of SU(2) and SL(2,R).

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