Pre-Calabi-Yau algebras as noncommutative Poisson structures

Iyudu, Natalia and Kontsevich, Maxim and Vlassopoulos, Yannis (2021) Pre-Calabi-Yau algebras as noncommutative Poisson structures. Journal of Algebra, 567. pp. 63-90. ISSN 0021-8693

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We give an explicit formula showing how the double Poisson algebra introduced in [14] 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 . 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 emphasises the special role of the fourth component of 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 for any associative algebra A.

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Journal Article
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Journal of Algebra
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Deposited On:
07 Jun 2021 10:30
Last Modified:
22 Nov 2022 10:19