Quantum groups and ribbon G-categories

Details Quantum groups and ribbon G-categories Quantum groups and ribbon G-categories

2001-03-03

arxiv.org/abs/math/0103017v1

Mathematics

Quantum Algebra

13 pages

Scientific paper

For a group G, the notion of a ribbon G-category was introduced by the second author in a previous work with a view towards constructing 3-dimensional homotopy quantum field theories (HQFT's) with target K(G,1). We discuss here how to derive ribbon G-categories from a simple complex Lie algebra g where G is the center of g. The construction is based on a study of representations of the quantum group $U_q(g)$ at a root of unity. Under certain assumptions on the root of unity, the resulting G-categories give rise to numerical invariants of pairs (a closed oriented 3-manifold M, an element of $H^1(M;G)$) and to 3-dimensional HQFT's.

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