Quantum groups and ribbon Gcategories
Abstract
For a group G, the notion of a ribbon Gcategory was introduced by the second author in a previous work with a view towards constructing 3dimensional homotopy quantum field theories (HQFT's) with target K(G,1). We discuss here how to derive ribbon Gcategories 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 Gcategories give rise to numerical invariants of pairs (a closed oriented 3manifold M, an element of $H^1(M;G)$) and to 3dimensional HQFT's.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2001
 arXiv:
 arXiv:math/0103017
 Bibcode:
 2001math......3017L
 Keywords:

 Quantum Algebra;
 Geometric Topology;
 57M10;
 57M25
 EPrint:
 13 pages