R-Matrix Poisson Algebras and Their Deformations

TL;DR

This paper classifies Poisson structures derived from classical r-matrices on modules over semisimple Lie algebras, explores their quantizations, and connects these findings to classical invariant theory.

Contribution

It provides a classification of Poisson structures from classical r-matrices and investigates their quantizations and invariant theory relations.

Findings

Classification of Poisson structures on modules over semisimple Lie algebras.

Analysis of quantizations of these Poisson structures.

Connection established between quantizations and classical invariant theory.

Abstract

We classify in this paper Poisson structures on modules over semisimple Lie algebras arising from classical r-matrices. We then study their quantizations and the relation to classical invariant theory.