Hawkins, Eli orcid.org/0000-0003-2054-3152 Operations on the Hochschild Bicomplex of a Diagram of Algebras. Working Paper. (Unpublished)
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.
Metadata
Authors/Creators: |
|
---|---|
Copyright, Publisher and Additional Information: | 60 pages |
Keywords: | math.CT, math.AT, math.RA, 18D50 (primary) 16E40 (Secondary) |
Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Mathematics (York) |
Depositing User: | Pure (York) |
Date Deposited: | 17 Feb 2020 09:40 |
Last Modified: | 06 Dec 2023 15:28 |
Status: | Unpublished |
Refereed: | No |
Related URLs: |