Calabi-Yau algebras and the shifted noncommutative symplectic structure
Rings and Algebras
2020-05-13 v2
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.
Keywords
Cite
@article{arxiv.1802.07423,
title = {Calabi-Yau algebras and the shifted noncommutative symplectic structure},
author = {Xiaojun Chen and Farkhod Eshmatov},
journal= {arXiv preprint arXiv:1802.07423},
year = {2020}
}