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Reconstruction of universal Drinfeld twists from representations

2004/10/20 by Christian Blohmann
Mathematics · Physics and Astronomy · #math.QA #hep-th #msc:17B37 #msc:80R50 #msc:17B10

paper · pdf · doi:10.1063/1.1901344

published as J.Math.Phys. 46 (2005) 053519 · 24 pages

arxiv created 2004/10/20 · arxiv updated 2009/12/01

Abstract

Universal Drinfeld twists are inner automorphisms which relate the coproduct of a quantum enveloping algebra to the coproduct of the undeformed enveloping algebra. Even though they govern the deformation theory of classical symmetries and have appeared in numerous applications, no twist for a semi-simple quantum enveloping algebra has ever been computed. It is argued that universal twists can be reconstructed from their well known representations. A method to reconstruct an arbitrary element of the enveloping algebra from its irreducible representations is developed. For the twist this yields an algebra valued generating function to all orders in the deformation parameter, expressed by a combination of basic and ordinary hypergeometric functions. An explicit expression for the universal twist of su(2) is given up to third order.

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