Quantizations of the $W$ Algebra W(2,2)

TL;DR

This paper presents the quantization of the W(2,2) algebra, building on prior work that characterized its modules and Lie bialgebra structures, to deepen understanding of its quantum properties.

Contribution

It provides a new quantization of the W(2,2) algebra, extending previous studies on its modules and Lie bialgebra structures.

Findings

Quantized version of W(2,2) algebra obtained

Enhanced understanding of its quantum module structures

Established Lie bialgebra properties in the quantum setting

Abstract

We quantize the $W$-algebra W(2,2), whose Verma modules, Harish-Chandra modules, irreducible weight modules and Lie bialgebra structures have been investigated and determined in a series of papers recently.