Regensburg 1998 – wissenschaftliches Programm

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 5: Quantisierung und Symmetrie

MP 5.8: Fachvortrag

Dienstag, 24. März 1998, 17:00–17:20, H45

Lattice Current Algebras at Roots of Unity — •Frank Haußer and Florian Nill — Inst. theor. Physik, FU-Berlin, Arnimallee 14, D-14195 Berlin

Based on the theory of Diagonal Crossed Products [1] we construct Hopf-Spin quantum chains [2] and lattice current algebras [3,4] at roots of unity. We prove [5] that for finite lattices the representation theory of such chains on a line coincides with Rep G and on a circle with Rep D(G), where D(G) denotes the quantum double of the underlying truncated quasi-quantum group G. We also construct localized coactions of D(G) on these quantum chains, thus generalizing the results of [2,3,4].

[1] F. Haußer, F. Nill, Diagonal Crossed Products by Duals of Quasi-Quantum Groups , q-alg/9708004; Doubles of Quasi-Quantum Groups, q-alg/9708023.

[2] F. Nill, K. Szlachanyi, Quantum Chains of Hopf Algebras with Quantum Double Cosymmetry, Comm. Math. Phys. 187 (1997) 159 - 200.

[3] A.Yu.Alekseev, L.D.Faddeev, J.Frohlich, V.Schomerus, Representation Theory of Lattice Current Algebras, q-alg/9604017.

[4] F. Nill, On the Structure of Monodromy Algebras and Drinfeld Doubles, Rev.Math.Phys. 9 (1997) 371-395.

[5] F. Haußer, F. Nill, Lattice Current Algebras at Roots of Unity, in preparation.