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