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 Science & Technology > Mathematics

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