Operations on the Hochschild Bicomplex of a Diagram of Algebras

Autor:	Hawkins, Eli
Rok vydání:	2020
Předmět:	Mathematics - Category Theory Mathematics - Algebraic Topology Mathematics - Rings and Algebras 18D50 (primary) 16E40 (Secondary)
Zdroj:	Adv. Math.428(2023), Paper No. 109156
Druh dokumentu:	Working Paper
DOI:	10.1016/j.aim.2023.109156
Popis:	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. Comment: 65 pages. Version 3: Published version. Minor corrections and improvements. I have changed "normalized'' to "reduced'' in order to be consistent with the literature
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2002.00886 Zobrazit plný text záznamu View this record from Arxiv