Hochschild (co)homology of the Dunkl operator quantization of $\Z_2$-singularity

TL;DR

This paper investigates the Hochschild (co)homology of Dunkl operator quantization related to $ ext{Z}_2$-singularities, introduces trace analysis, and establishes a local algebraic index formula.

Contribution

It provides a detailed analysis of Hochschild (co)homology for Dunkl operator quantizations and derives a local algebraic index formula, advancing understanding of singularity quantizations.

Findings

Computed Hochschild (co)homology groups for the algebra.

Analyzed traces on the algebra.

Proved a local algebraic index formula.

Abstract

We study Hochschild (co)homology groups of the Dunkl operator quantization of $\Z_2$-singularity constructed by Halbout and Tang. Further, we study traces on this algebra and prove a local algebraic index formula.