Planar System and $w_\infty$ Algebra

TL;DR

This paper explores the symmetry structures of exotic particles in noncommutative 2D phase space, revealing a deformed $C_{\lambda}$-extended Heisenberg algebra and $ ext{ extomega}_ ext{infty}$ symmetry, contributing to mathematical physics.

Contribution

It introduces a deformed algebra and symmetry framework for exotic particles in noncommutative phase space, advancing theoretical understanding.

Findings

Realization of deformed $C_{\lambda}$-extended Heisenberg algebra

Identification of $ ext{ extomega}_ extinfty$ symmetry in the system

Connection between noncommutative geometry and exotic particle symmetries

Abstract

We study the exotic particles symmetry in the background of noncommutative two-dimensional phase-space leading to realize in physicswise the deformed version of $C_{\lambda}$-extended Heisenberg algebra and $\om_\infty$ symmetry.