City Research Online

On the perturbation algebra

Chuang, J. and Lazarev, A. (2018). On the perturbation algebra. Journal of Algebra, 519, pp. 130-148. doi: 10.1016/j.jalgebra.2018.10.032

Abstract

We introduce a certain differential graded bialgebra, neither commutative nor cocommutative, that governs perturbations of a differential on complexes supplied with an abstract Hodge decomposition. This leads to a conceptual treatment of the Homological Perturbation Lemma and its multiplicative version. As an application we give an explicit form of the decomposition theorem for A∞ algebras and A∞ modules and, more generally, for twisted objects in differential graded categories.

Publication Type: Article
Additional Information: © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords: Abstract Hodge decomposition, differential graded algebra, Maurer-Cartan element
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/20960
[img] Text - Accepted Version
This document is not freely accessible until 7 November 2019 due to copyright restrictions.
Available under License Creative Commons Attribution Non-commercial No Derivatives.

To request a copy, please use the button below.

Request a copy

Export

Downloads

Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login