Hochschild cochains as a Frobenius algebra

Jerry Lodder

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arXiv · 1409.4825

Hochschild cochains as a Frobenius algebra

Jerry Lodder

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Abstract

We construct a Frobenius algebra structure on the Hochschild cochains of a group ring k[G] that extends the known structure of a <1, 2> topological quantum field theory on HH^0(k[G]; k[G]), k a field and G a finite group. The convolution product extends to the homotopy commutative Gerstenhaber product on cochains, the Frobenius coproduct extends to a coproduct on the chain complex for Hochschild homology, and there is a pairing on Hochschild cocahins satisfying Frobenius associativity. The pairing, however, degenerates on a certain subcomplex of Hochschild cochains. The cochain complex for group cohomology under the simplicial cup product occurs as a homotopy commutative subalgebra of the Hochschild cochain complex under the Gerstenhaber product.

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Jerry Lodder. 2014-09-16. Hochschild cochains as a Frobenius algebra. https://arxiv.org/abs/1409.4825

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