On the $C_{\lambda}$-extended $w_{\infty}$-symmetry

TL;DR

This paper introduces a new deformed $w_{ olinebreak\infty}$-algebra derived from $C_{\lambda}$-extended oscillator algebras, expanding the algebraic structures related to $sp(2)$ symmetries.

Contribution

It constructs a novel deformed $w_{\infty}$-algebra from $C_{\lambda}$-extended oscillator algebras, providing an infinite-dimensional extension of $sp(2)$ realization.

Findings

Derived a new deformed $w_{\infty}$-algebra from $C_{\lambda}$-extended oscillator algebras.

Expressed the algebra generators via creation and annihilation operators.

Extended the realization of $sp(2)$ algebra to an infinite-dimensional setting.

Abstract

Starting from the $C_{\lambda}$-extended oscillator algebras, we obtain a new deformed $w_{\infty}$-algebra. More precisely, we show that the $C_{\lambda}$-extended $w_{\infty}$-algebra generators may be expressed via the annihilation and creation operators of the $C_{\lambda}$-extended oscillator algebras $a$ and $a^{\dagger}$ as an infinite-dimensional extension of the realization of $sp(2)$ algebra.