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A discrete approach to topological quantum field theories. (English) Zbl 0795.17035
A rather general scheme for constructing three-dimensional Euclidean topological quantum field theories is described. A basic construction uses \(6j\)-symbols defined for a finite semisimple tensor category of representations of some bialgebra. The examples of the algebra of functions over a finite group, and the group algebra of a finite group, and the quantum deformation of the enveloping algebra of a simple Lie algebra are discussed. An explicit connection with the Dijkgraaf-Witten model is established.

MSC:
17B81 Applications of Lie (super)algebras to physics, etc.
81T20 Quantum field theory on curved space or space-time backgrounds
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