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

TL;DR

This paper introduces new algebraic structures using $C_{\lambda}$-extended oscillator algebras, including realizations of FFZ algebra, quantum $U_t(sl(2))$, and a deformed Virasoro algebra, expanding the mathematical framework of these systems.

Contribution

It presents novel realizations of algebraic structures through $C_{\lambda}$-extended oscillator algebras, including connections to quantum groups and deformed Virasoro algebra.

Findings

Realization of FFZ algebra via $C_{\lambda}$-extended oscillator algebras

Construction of quantum $U_t(sl(2))$ algebra from these realizations

Introduction of a new deformed Virasoro algebra

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.