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

## TL;DR

This paper explores the gravity algebra structures on negative cyclic homology and cyclic cohomology across various algebra classes, revealing their interrelations and extending understanding of algebraic structures in mathematical physics.

## Contribution

It introduces the gravity algebra structure on negative cyclic homology for several algebra classes and discusses their interrelations under specific conditions.

## Key findings

- Gravity algebra structures are established on negative cyclic homology of Calabi-Yau and related algebras.
- Relationships among these gravity algebras are analyzed under certain conditions.
- The study broadens the understanding of algebraic structures in the context of cyclic homology.

## 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.