• Corpus ID: 189928397

Pre-Calabi-Yau algebras and double Poisson brackets

@article{Iyudu2019PreCalabiYauAA,
  title={Pre-Calabi-Yau algebras and double Poisson brackets},
  author={Natalia Iyudu and Maxim Kontsevich and Yannis Vlassopoulos},
  journal={arXiv: Rings and Algebras},
  year={2019}
}
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… 

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