Calabi-Yau algebras and the shifted noncommutative symplectic structure

Xiaojun Chen; Farkhod Eshmatov

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arXiv · 1802.07423

Calabi-Yau algebras and the shifted noncommutative symplectic structure

Xiaojun Chen·Farkhod Eshmatov

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Abstract

In this paper we show that for a Koszul Calabi-Yau algebra, there is a shifted bi-symplectic structure in the sense of Crawley-Boevey-Etingof-Ginzburg, on the cobar construction of its co-unitalized Koszul dual coalgebra, and hence its DG representation schemes, in the sense of Berest-Khachatryan-Ramadoss, have a shifted symplectic structure in the sense of Pantev-To\"en-Vaqui\'e-Vezzosi.

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Xiaojun Chen, Farkhod Eshmatov. 2018-02-21. Calabi-Yau algebras and the shifted noncommutative symplectic structure. https://arxiv.org/abs/1802.07423

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