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Zbl 0828.57012
Beliakova, Anna; Durhuus, Bergfinnur
(Belyakova, A.)
Topological quantum field theory and invariants of graphs for quantum groups. (English)
[J] Commun. Math. Phys. 167, No.2, 395-429 (1995). ISSN 0010-3616; ISSN 1432-0916/e

Summary: On the basis of generalized $6j$-symbols we give a formulation of topological quantum field theories for 3-manifolds including observables in the form of coloured graphs. It is shown that the $6j$-symbols associated with deformations of the classical groups at primitive even roots of unity provide examples of this construction. Calculational methods are developed which, in particlar, yield the dimensions of the state spaces as well as a rather simple proof of the relation, previously found by Turaev and Walker for the case of $U_q (\text {sl} (2, \bbfC))$, between these models and corresponding ones based on the ribbon graph construction of Reshetikhin and Turaev.

MSC 2000:: *57N10 Topology of general 3-manifolds
81T40 Two-dimensional field theories, etc.
81R50 Quantum groups and related algebraic methods in quantum theory

Keywords: generalized $6j$-symbols; $U\sb q (\text {sl} (2, \bbfC))$; quantum group associated to $\text {SL} (2, \bbfC)$; topological quantum field theories; 3-manifolds; coloured graphs; ribbon graph

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