Tensor products of quantized tilting modules |
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Authors: | Henning Haahr Andersen |
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Institution: | (1) Matematisk Institut, Aarhus Universitet, DK-8000 Aarhus C, Denmark |
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Abstract: | LetU
k denote the quantized enveloping algebra corresponding to a finite dimensional simple complex Lie algebraL. Assume that the quantum parameter is a root of unity ink of order at least the Coxeter number forL. Also assume that this order is odd and not divisible by 3 if typeG
2 occurs. We demonstrate how one can define a reduced tensor product on the familyF consisting of those finite dimensional simpleU
k-modules which are deformations of simpleL and which have non-zero quantum dimension. This together with the work of Reshetikhin-Turaev and Turaev-Wenzl prove that (U
k,F) is a modular Hopf algebra and hence produces invariants of 3-manifolds. Also by recent work of Duurhus, Jakobsen and Nest it leads to a general topological quantum field theory. The method of proof explores quantized analogues of tilting modules for algebraic groups. |
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Keywords: | |
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