Operations on the Hochschild Bicomplex of a Diagram of Algebras

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DateUnpublished - 3 Feb 2020
Original languageEnglish

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 asimplicial subcomplex and its cohomology. This structure governs deformations of diagrams of algebras through the Maurer-Cartan equation.

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60 pages

    Research areas

  • math.CT, math.AT, math.RA, 18D50 (primary) 16E40 (Secondary)

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