Non-commutative Poisson Structures on quantum torus orbifolds

TL;DR

This paper investigates the Hochschild cohomology, Gerstenhaber algebra structures, and Poisson cohomology of quantum torus orbifolds formed by finite group actions, revealing new insights into their non-commutative geometric properties.

Contribution

It provides a detailed analysis of Hochschild and Poisson cohomology for quantum torus orbifolds under finite group actions, a novel study in non-commutative geometry.

Findings

Computed Hochschild cohomology for quantum torus orbifolds.

Analyzed Gerstenhaber algebra structures in this context.

Determined Poisson cohomology for these non-commutative spaces.

Abstract

We study the Hochschild cohomology and the Gerstenhaber algebra structure on the algebraic non-commutative torus/quantum torus orbifolds resulting by the action of finite subgroups of $SL_2(\mathbb Z)$. We also examine the Poisson structures and compute the Poisson cohomology.