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

Florian Nill·Kornel Szlachanyi
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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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Florian Nill, Kornel Szlachanyi. 1995-07-31. Quantum Chains of Hopf Algebras with Order-Disorder Fields and Quantum Double Symmetry. https://arxiv.org/abs/hep-th/9507174

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