LINK INVARIANTS ASSOCIATED TO TQFT’S WITH FINITE GAUGE GROUPS

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Abstract
It has already been rigorously established that if G is a finite group and α∈H4(G; ℤ), there is an associated 2+1-dimensional topological quantum field theory. In the case α=0, there is a Hopf algebra associated to the theory. We give an intuitive geometric solution to the Yang-Baxter equation for and go on to show that is a modular Hopf algebra. We also prove a structure theorem concerning the Verlinde algebra which is seen to correspond to an algebra structure on the space of finite dimensional representations of . A knowledge of this structure aids the development of the skein theory for the link invariants of Reshetikhin and Turaev which are associated to .

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