Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Pre-Calabi-Yau algebras as noncommutative Poisson structures
AU - Iyudu, Natalia
AU - Kontsevich, Maxim
AU - Vlassopoulos, Yannis
PY - 2021/2/1
Y1 - 2021/2/1
N2 - 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.
AB - 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.
U2 - 10.1016/j.jalgebra.2020.08.029
DO - 10.1016/j.jalgebra.2020.08.029
M3 - Journal article
VL - 567
SP - 63
EP - 90
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
ER -