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arXiv · 2002.00886

Operations on the Hochschild Bicomplex of a Diagram of Algebras

Eli Hawkins
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Abstract

A diagram of algebras is a functor valued in a category of associative algebras. I construct an operad acting on the Hochschild bicomplex of a diagram of algebras. Using this operad, I give a direct proof that the Hochschild cohomology of a diagram of algebras is a Gerstenhaber algebra. I also show that the total complex is an $L_\infty$-algebra. The same results are true for the reduced and asimplicial subcomplexes and asimplicial cohomology. This structure governs deformations of diagrams of algebras through the Maurer-Cartan equation.

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BibTeXRIS

Eli Hawkins. 2020-02-03. Operations on the Hochschild Bicomplex of a Diagram of Algebras. https://doi.org/10.1016/j.aim.2023.109156

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