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

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 $a^{†}$ as an infinite-dimensional extension of the realization of $sp(2)$ algebra.

12pages (submitted)