Operations on the Hochschild bicomplex of a diagram of algebras

Eli Hawkins

doi:10.1016/j.aim.2023.109156

Operations on the Hochschild bicomplex of a diagram of algebras

Eli Hawkins

Mathematics

Research output: Contribution to journal › Article › peer-review

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-infinity 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.

Original language	English
Article number	109156
Number of pages	80
Journal	Advances in Mathematics
Volume	428
Early online date	19 Jun 2023
DOIs	https://doi.org/10.1016/j.aim.2023.109156
Publication status	Published - 1 Sept 2023

Bibliographical note

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10.1016/j.aim.2023.109156Licence: CC BY-NC-ND

1-s2.0-S0001870823002992-main
© 2023 The Author(s)
Final published version, 0.98 MBLicence: CC BY-NC-ND

Cite this

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