TOPOLOGICAL QUANTUM-FIELD THEORIES FROM GENERALIZED 6J-SYMBOLS

Given an associative algebra with a distinguished finite set of representations that is closed under a (deformed) tensor product, and satisfies some technical assumptions, we define generalized 6j-symbols, and show that they can be associated, in a natural way, with certain labeled tetrahedra. Given a 3-dimensional compact oriented manifold M with boundary partial derivative M = SIGMA we choose an arbitrary triangulation tau of M and exploit the above correspondence between 6j-symbols and labeled tetrahedra to construct a vectorspace U(SIGMA) and a vector Z(M) is-an-element-of U(SIGMA), independent of tau, and fulfilling the axioms of a topological quantum field theory as formulated by Atiyah [11]. Examples covered by our approach are quantum groups corresponding to the classical simple Lie algebras as well as, expectedly, chiral algebras of 2-dimensional rational conformal field theories.