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  Pre-Calabi-Yau algebras as noncommutative Poisson structures

Iyudu, N., Kontsevich, M., & Vlassopoulos, Y. (2021). Pre-Calabi-Yau algebras as noncommutative Poisson structures. Journal of Algebra, 567, 63-90. doi:10.1016/j.jalgebra.2020.08.029.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0007-A23C-F Version Permalink: https://hdl.handle.net/21.11116/0000-000E-09C5-A
Genre: Journal Article

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 Creators:
Iyudu, Natalia1, Author           
Kontsevich, Maxim1, Author           
Vlassopoulos, Yannis1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Rings and Algebras
 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 $A$.

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Language(s): eng - English
 Dates: 2021
 Publication Status: Issued
 Pages: 28
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1906.07134
DOI: 10.1016/j.jalgebra.2020.08.029
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Title: Journal of Algebra
  Abbreviation : J. Algebra
Source Genre: Journal
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Publ. Info: Elsevier
Pages: - Volume / Issue: 567 Sequence Number: - Start / End Page: 63 - 90 Identifier: -