Quantum groups and ribbon G-categories
Abstract
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- March 2001
- DOI:
- 10.48550/arXiv.math/0103017
- arXiv:
- arXiv:math/0103017
- Bibcode:
- 2001math......3017L
- Keywords:
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- Quantum Algebra;
- Geometric Topology;
- 57M10;
- 57M25
- E-Print:
- 13 pages