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

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.