**The International Conference on
**

Secondary Calculus and Cohomological Physics,

Moscow, August 24 - August 31, 1997

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On some Hochschild cohomology classes of fusion algebras

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A. A. Davydov

**Abstract:** The obstructions for an arbitrary fusion algebra to be a fusion algebra of some semisimple monoidal category are constructed. Those obstructions lie in groups which are closely related to the Hochschild cohomology of fusion algebras with coefficients in the $K$-theory of the ground (algebraically closed) field.

The special attention is devoted to the case of fusion algebra of invariants of finite group action on the group ring of abelian group.

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