Let A be a finite dimensional, unital, and associative algebra which is endowed with a non-degenerate and invariant inner product. We give an explicit description of an action of cyclic Sullivan chord diagrams on the normalized Hochschild cochain complex of A. As a corollary, the Hochschild cohomology of A becomes a Frobenius algebra which is endowed with a compatible BV operator. If A is also commutative, then the discussion extends to an action of general Sullivan chord diagrams. Some implications of this are discussed.
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