Gravity algebra structure on the negative cyclic homology of Calabi–Yau algebras

Chen, Xiaojun; Eshmatov, Farkhod; Liu, Leilei

doi:10.1016/j.geomphys.2019.103522

Cited by 3 publications

(4 citation statements)

References 36 publications

(61 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The above theorem generalizes Xu's result in [43] and the first two authors' result joint with Eshmatov in [11] where only unimodular Poisson manifolds are considered.…”

Section: Introductionsupporting

confidence: 80%

“…We now reach to the proof of the following two theorems, which supersede the results obtained in [10,11] for unimodular Poisson algebras. with semi-simple modular vector, the following…”

Section: Koszul Duality and Deformation Quantizationmentioning

confidence: 56%

“…In [11], the first two authors of the current paper together with Eshmatov showed that the negative cyclic Poisson homology of a unimodular Poisson algebra, and the the cyclic Poisson cohomology of a unimodular Frobenius Poisson algebra, have a gravity algebra structure. As we said in the beginning, the gravity algebra structure play an important role in the study of equivariant TCFT (see Getzler [17,18]).…”

Section: The Gravity Algebra Structurementioning

confidence: 78%

“…The purpose of this result is to generalize the result of [11] to the case where the modular vector is semi-simple (see Theorem 7.4). Definition 4.1 (Gravity algebra).…”

Section: The Gravity Algebra Structurementioning

confidence: 90%

See 3 more Smart Citations

Batalin-Vilkovisky algebra structure on Poisson manifolds with semi-simple modular symmetry

Chen¹,

Liu²,

Yu³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

We study the "twisted" Poincaré duality of smooth Poisson manifolds, and show that, if the modular symmetry is semisimple, that is, the modular vector is diagonalizable, there is a mixed complex associated to the Poisson complex which, combining with the twisted Poincaré duality, gives a Batalin-Vilkovisky algebra structure on the Poisson cohomology, and a gravity algebra structure on the negative cyclic Poisson homology. This generalizes the previous results obtained by Xu et al for unimodular Poisson algebras. We also show that these two algebraic structures are preserved under Kontsevich's deformation quantization, and in the case of polynomial algebras they are also preserved by Koszul duality.

show abstract

“…The above theorem generalizes Xu's result in [43] and the first two authors' result joint with Eshmatov in [11] where only unimodular Poisson manifolds are considered.…”

Section: Introductionsupporting

confidence: 80%

“…We now reach to the proof of the following two theorems, which supersede the results obtained in [10,11] for unimodular Poisson algebras. with semi-simple modular vector, the following…”

Section: Koszul Duality and Deformation Quantizationmentioning

confidence: 56%

Section: The Gravity Algebra Structurementioning

confidence: 78%

“…The purpose of this result is to generalize the result of [11] to the case where the modular vector is semi-simple (see Theorem 7.4). Definition 4.1 (Gravity algebra).…”

Section: The Gravity Algebra Structurementioning

confidence: 90%

See 2 more Smart Citations