Calabi-Yau algebras viewed as deformations of Poisson algebras

TL;DR

This paper introduces a family of 3-Calabi-Yau algebras defined via potentials and computes their Hochschild homology using Poisson homology, even with non-isolated singularities.

Contribution

It establishes a connection between Calabi-Yau algebras and Poisson homology, providing explicit computations for algebras with complex singularities.

Findings

Explicit Hochschild homology computations for certain Calabi-Yau algebras

Demonstrates the use of Poisson homology in algebraic deformation analysis

Shows Calabi-Yau algebras can be viewed as deformations of Poisson algebras

Abstract

We define a family of 3-Calabi-Yau algebras by potentials. For some of these algebras, we explicitly compute the Hochschild homology with the help of Poisson homology. The point is that the Poisson potential has non-isolated singularities.