5 citations · 6 across the 6 of their papers we have counts for
7 papers
Shifted double Poisson structures and noncommutative Poisson extensions
Leilei Liu, Jieheng Zeng, Hu Zhao
We develop a theory of noncommutative Poisson extensions. For an augmented dg algebra \(A\), we show that any shifted double Poisson bracket on \(A\) induces a graded Lie algebra s…
DG singular equivalence and singular locus
Leilei Liu, Jieheng Zeng
For a commutative Gorenstein Noetherian ring , we construct an affine scheme solely from DG singularity category of such that there is a finite surjective mo…
Tilting objects in singularity categories of toric Gorenstein varieties
Xiaojun Chen, Leilei Liu, Jieheng Zeng
We study certain toric Gorenstein varieties with isolated singularities which are the quotient spaces of generic unimodular representations by the one-dimensional torus, or by the…
Batalin-Vilkovisky algebra structure on Poisson manifolds with diagonalizable modular symmetry
Xiaojun Chen, Leilei Liu, Sirui Yu +1
We study the ``twisted" Poincaré duality of smooth Poisson manifolds, and show that, if the modular vector field is diagonalizable, then there is a mixed complex associated to the…
Twisted bi-symplectic structure on Koszul twisted Calabi-Yau algebras
Xiaojun Chen, Alimjon Eshmatov, Farkhod Eshmatov +1
For a Koszul Artin-Schelter regular algebra (also called twisted Calabi-Yau algebra), we show that it has a "twisted" bi-symplectic structure, which may be viewed as a noncommutati…
Koszul duality and the Hochschild cohomology of Artin-Schelter regular algebras
Leilei Liu
We identify two Batalin-Vilkovisky algebra structures, one obtained by Kowalzig and Krahmer on the Hochschild cohomology of an Artin-Schelter regular algebra with semisimple Nakaya…
Gravity algebra structure on the negative cyclic homology of Calabi-Yau algebras
Xiaojun Chen, Farkhod Eshmatov, Leilei Liu
In this paper, we study the gravity algebra structure on the negative cyclic homology or the cyclic cohomology of several classes of algebras. These algebras include: Calabi-Yau al…