Quantum Chains of Hopf Algebras with Order-Disorder Fields and Quantum Double Symmetry

1995/07/31 by Florian Nill, Nill, Florian, Kornel Szlachanyi +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9507174

40 pages, plain TEX

arxiv created 1995/07/31 · arxiv updated 2009/11/30

Abstract

Given a finite dimensional C-*-Hopf algebra H and its dual H^ we construct the infinite crossed product A=... x H x H^ x H x ... and study its representations. A is the observable algebra of a generalized spin model with H-order and H^-disorder symmetries. By pointing out that A possesses a certain compressibility property we can classify all DHR-sectors of A --- relative to some Haag dual vacuum representation --- and prove that their symmetry is described by the Drinfeld double D(H). Complete, irreducible, translation covariant field algebra extensions F > A are shown to be in one-to-one correspondence with cohomology classes of 2-cocycles u in D(H) @ D(H).

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