English

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}
}