Derivations of a family of quantum second Weyl algebras

TL;DR

This paper investigates primitive quotients of quantum positive parts of Lie algebras, specifically for type G2, and computes their derivation Lie algebras, contributing to the understanding of quantum Weyl algebra analogues.

Contribution

It provides a detailed analysis of primitive quotients of quantum G2 algebras and explicitly computes their derivation Lie algebras, advancing the theory of quantum Weyl algebra analogues.

Findings

Primitive quotients of quantum G2 algebras are characterized.

The Lie algebra of derivations for these quotients is explicitly computed.

Results deepen understanding of quantum analogues of Weyl algebras.

Abstract

In view of a well-known theorem of Dixmier, its is natural to consider primitive quotients of $U_q^+(\mathfrak{g})$ as quantum analogues of Weyl algebras. In this work, we study these primitive quotients in the $G_2$ case and compute their Lie algebra of derivations.