Abstract / Description of output
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 $A$.
Original language | English |
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Publisher | ArXiv |
Pages | 1-24 |
Number of pages | 24 |
Publication status | Published - 17 Jun 2019 |
Keywords / Materials (for Non-textual outputs)
- math.RA
- 16A22, 16S37, 16Y99