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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

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On the perturbation algebra. / Chuang, Joseph; Lazarev, Andrey.
In: Journal of Algebra, Vol. 519, 01.02.2019, p. 130-148.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Chuang, J & Lazarev, A 2019, 'On the perturbation algebra', Journal of Algebra, vol. 519, pp. 130-148. https://doi.org/10.1016/j.jalgebra.2018.10.032

APA

Chuang, J., & Lazarev, A. (2019). On the perturbation algebra. Journal of Algebra, 519, 130-148. https://doi.org/10.1016/j.jalgebra.2018.10.032

Vancouver

Chuang J, Lazarev A. On the perturbation algebra. Journal of Algebra. 2019 Feb 1;519:130-148. Epub 2018 Nov 7. doi: 10.1016/j.jalgebra.2018.10.032

Author

Chuang, Joseph ; Lazarev, Andrey. / On the perturbation algebra. In: Journal of Algebra. 2019 ; Vol. 519. pp. 130-148.

Bibtex

@article{ed355ae2d4504a97b844010a3bcba2c8,
title = "On the perturbation algebra",
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",
keywords = "Abstract Hodge decomposition, Differential graded algebra, Maurer–Cartan element",
author = "Joseph Chuang and Andrey Lazarev",
note = "This is the author{\textquoteright}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",
year = "2019",
month = feb,
day = "1",
doi = "10.1016/j.jalgebra.2018.10.032",
language = "English",
volume = "519",
pages = "130--148",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "ELSEVIER ACADEMIC PRESS INC",

}

RIS

TY - JOUR

T1 - On the perturbation algebra

AU - Chuang, Joseph

AU - Lazarev, Andrey

N1 - 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

PY - 2019/2/1

Y1 - 2019/2/1

N2 - 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

AB - 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

KW - Abstract Hodge decomposition

KW - Differential graded algebra

KW - Maurer–Cartan element

U2 - 10.1016/j.jalgebra.2018.10.032

DO - 10.1016/j.jalgebra.2018.10.032

M3 - Journal article

VL - 519

SP - 130

EP - 148

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -