On the perturbation algebra

Chuang, Joseph and Lazarev, Andrey (2019) On the perturbation algebra. Journal of Algebra, 519. pp. 130-148. ISSN 0021-8693

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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

Item Type:
Journal Article
Journal or Publication Title:
Journal of Algebra
Additional Information:
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
Uncontrolled Keywords:
?? abstract hodge decompositiondifferential graded algebramaurer–cartan elementalgebra and number theory ??
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Deposited On:
07 Nov 2018 14:18
Last Modified:
15 Jul 2024 18:36