Hochschild homology of structured algebras

By Nathalie Wahl, Craig Westerland. 2011

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We give a general method for constructing explicit and natural operations on the Hochschild complex of algebras over any PROP with $A_\infty$--multiplication---we think of such algebras as $A_\infty$--algebras "with extra structure". As applications, we obtain an integral version of the Costello-Kontsevich-Soibelman moduli space action on the Hochschild complex of open TCFTs, the Tradler-Zeinalian action of Sullivan diagrams on the Hochschild complex of strict Frobenius algebras, and give applications to string topology in characteristic zero. Our main tool is a generalization of the Hochschild complex.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9d4cc7750340a74135f7dca4bda7c1c485b4b0c4