Pre-Calabi-Yau algebras as noncommutative Poisson structures

JOURNAL OF ALGEBRA

卷:567

Article

Iyudu, Natalia¹  Kontsevich, Maxim²  Vlassopoulos, Yannis² 

[1] Univ Edinburgh, Sch Math, James Clerk Maxwell Bldg,Kings Bldg, Edinburgh EH9 3FD, Midlothian, Scotland

[2] Inst Hautes Etud Sci, 35 Route Chartres, F-91440 Bures Sur Yvette, France

关键词: A-infinity structure;    Pre-Calabi-Yau algebra;    Inner product;    Cyclic invariance;    Graded pre-Lie algebras;    Necklace bracket;    Maurer-Cartan equation;    Double Poisson brackets;   

DOI  :  10.1016/j.jalgebra.2020.08.029

来源: Elsevier

【 摘 要 】

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 A circle plus 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 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 (Rep(n)A)(Gln) for any associative algebra A. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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