Calabi-Yau algebras and the shifted noncommutative symplectic structure

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-Toën-Vaquié-Vezzosi.

References in corpus (2)

• Calabi-Yau algebras
• Calabi-Yau Deformations and Negative Cyclic Homology

Cited by in corpus (1)

• Shifted bisymplectic and double Poisson structures on non-commutative derived prestacks