New algebraic structures in the $C_{\lambda }$-extended Hamiltonian system

Abstract

A realization of various algebraic structures in terms of the $C_{\lambda }$-extended oscillator algebras is introduced. In particular, the $C_{\lambda }$-extended oscillator algebras realization of Fairlie-Fletcher-Zachos (FFZ)algebra is given. This latter lead easily to the realization of the quantum $U_t(sl(2))$ algebra. The new deformed Virasoro algebra is also presented.

10 pages