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

Abstract

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 algebras, symmetric Frobenius algebras, unimodular Poisson algebras, and unimodular Frobenius Poisson algebras. The relationships among these gravity algebras are also discussed under some additional conditions.

arXiv comment26 pages. Corrected some inaccuracies. arXiv admin note: text overlap with arXiv:1701.06112

References in corpus (10)

• Deformation quantization of Poisson manifolds, I
• Calabi-Yau algebras
• Batalin-Vilkovisky algebras and two-dimensional topological field theories
• String Topology
• Relative formality theorem and quantisation of coisotropic submanifolds
• Two-dimensional topological gravity and equivariant cohomology
• Deformation quantization with traces
• Bimodules and branes in deformation quantization
• Compatibility with cap-products in Tsygan's formality and homological Duflo isomorphism
• Poisson cohomology, Koszul duality, and Batalin-Vilkovisky algebras

Cited by in corpus (3)

• On the embedding complexity of Liouville manifolds
• Endomorphism operads of functors
• A reduction of the string bracket to the loop product