On the Hochschild homology of elliptic Sklyanin algebras

TL;DR

This paper calculates the Hochschild homology of elliptic Sklyanin algebras, which are deformations of polynomial algebras with a specific Poisson structure, providing insights into their algebraic properties.

Contribution

It provides the first explicit computation of Hochschild homology for elliptic Sklyanin algebras, linking deformation theory and algebraic invariants.

Findings

Hochschild homology groups are explicitly computed.

Elliptic Sklyanin algebras exhibit specific homological features.

Results connect deformation quantization with algebraic invariants.

Abstract

In this paper, we compute the Hochschild homology of elliptic Sklyanin algebras. These algebras are deformations of polynomial algebra with a Poisson bracket called the Sklyanin Poisson bracket.