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  • 1703.05296

    Rights statement: This is the author’s version of a work that was accepted for publication in Journal of Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Algebra, 519, 2019 DOI: 10.1016/j.jalgebra.2018.10.032

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On the perturbation algebra

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>1/02/2019
<mark>Journal</mark>Journal of Algebra
Volume519
Number of pages19
Pages (from-to)130-148
Publication statusPublished
Early online date7/11/18
Original languageEnglish

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-infinity algebras and A-infinity modules and, more generally, for twisted objects in differential graded categories

Bibliographic note

This is the author’s version of a work that was accepted for publication in Journal of Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Algebra, 519, 2019 DOI: 10.1016/j.jalgebra.2018.10.032