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  • 1906.07134v1

    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 inJournal of Algebra, ?, ?, 2021 DOI: 10.1016/j.jalgebra.2020.08.029

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Pre-Calabi-Yau algebras and double Poisson brackets

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Pre-Calabi-Yau algebras and double Poisson brackets. / Iyudu, Natalia; Kontsevich, Maxim; Vlassopoulos, Yannis.
In: Journal of Algebra, 01.02.2021, p. 63-90.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Iyudu, N, Kontsevich, M & Vlassopoulos, Y 2021, 'Pre-Calabi-Yau algebras and double Poisson brackets', Journal of Algebra, pp. 63-90. https://doi.org/10.1016/j.jalgebra.2020.08.029

APA

Iyudu, N., Kontsevich, M., & Vlassopoulos, Y. (2021). Pre-Calabi-Yau algebras and double Poisson brackets. Journal of Algebra, 63-90. https://doi.org/10.1016/j.jalgebra.2020.08.029

Vancouver

Iyudu N, Kontsevich M, Vlassopoulos Y. Pre-Calabi-Yau algebras and double Poisson brackets. Journal of Algebra. 2021 Feb 1;63-90. Epub 2020 Sept 16. doi: 10.1016/j.jalgebra.2020.08.029

Author

Iyudu, Natalia ; Kontsevich, Maxim ; Vlassopoulos, Yannis. / Pre-Calabi-Yau algebras and double Poisson brackets. In: Journal of Algebra. 2021 ; pp. 63-90.

Bibtex

@article{9b9132ff0eb84566ae72c8d8a264f190,
title = "Pre-Calabi-Yau algebras and double Poisson brackets",
abstract = "We give an explicit formula showing how the double Poisson algebra introduced in \cite{VdB} appears as a particular part of a pre-Calabi-Yau structure, i.e. cyclically invariant, with respect to the natural inner form, solution of the Maurer-Cartan equation on $A\oplus A^*$. Specific part of this solution is described, which is in one-to-one correspondence with the double Poisson algebra structures. The result holds for any associative algebra $A$ and emphasizes the special role of the fourth component of a pre-Calabi-Yau structure in this respect. As a consequence we have that appropriate pre-Calabi-Yau structures induce a Poisson brackets on representation spaces $({\rm Rep}_n A)^{Gl_n}$ for any associative algebra $A$. ",
keywords = "math.RA, 16A22, 16S37, 16Y99",
author = "Natalia Iyudu and Maxim Kontsevich and Yannis Vlassopoulos",
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 inJournal of Algebra, ?, ?, 2021 DOI: 10.1016/j.jalgebra.2020.08.029",
year = "2021",
month = feb,
day = "1",
doi = "10.1016/j.jalgebra.2020.08.029",
language = "English",
pages = "63--90",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "ELSEVIER ACADEMIC PRESS INC",

}

RIS

TY - JOUR

T1 - Pre-Calabi-Yau algebras and double Poisson brackets

AU - Iyudu, Natalia

AU - Kontsevich, Maxim

AU - Vlassopoulos, Yannis

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 inJournal of Algebra, ?, ?, 2021 DOI: 10.1016/j.jalgebra.2020.08.029

PY - 2021/2/1

Y1 - 2021/2/1

N2 - We give an explicit formula showing how the double Poisson algebra introduced in \cite{VdB} appears as a particular part of a pre-Calabi-Yau structure, i.e. cyclically invariant, with respect to the natural inner form, solution of the Maurer-Cartan equation on $A\oplus A^*$. Specific part of this solution is described, which is in one-to-one correspondence with the double Poisson algebra structures. The result holds for any associative algebra $A$ and emphasizes the special role of the fourth component of a pre-Calabi-Yau structure in this respect. As a consequence we have that appropriate pre-Calabi-Yau structures induce a Poisson brackets on representation spaces $({\rm Rep}_n A)^{Gl_n}$ for any associative algebra $A$.

AB - We give an explicit formula showing how the double Poisson algebra introduced in \cite{VdB} appears as a particular part of a pre-Calabi-Yau structure, i.e. cyclically invariant, with respect to the natural inner form, solution of the Maurer-Cartan equation on $A\oplus A^*$. Specific part of this solution is described, which is in one-to-one correspondence with the double Poisson algebra structures. The result holds for any associative algebra $A$ and emphasizes the special role of the fourth component of a pre-Calabi-Yau structure in this respect. As a consequence we have that appropriate pre-Calabi-Yau structures induce a Poisson brackets on representation spaces $({\rm Rep}_n A)^{Gl_n}$ for any associative algebra $A$.

KW - math.RA

KW - 16A22, 16S37, 16Y99

U2 - 10.1016/j.jalgebra.2020.08.029

DO - 10.1016/j.jalgebra.2020.08.029

M3 - Journal article

SP - 63

EP - 90

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -