Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces

TL;DR

This paper investigates how conformal-Poincare and Galilean symmetries can be deformed on canonical noncommutative spaces, leading to new algebraic structures and Hopf algebras, with specific cases reproducing undeformed symmetries.

Contribution

It introduces a general framework for deformed symmetries on noncommutative spaces, including new algebraic structures and twist representations for certain parameter choices.

Findings

Derived deformed generators with free parameters

Identified conditions for undeformed algebra recovery

Constructed associated Hopf algebra and twist functions

Abstract

We study the general deformed conformal-Poincare (Galilean) symmetries consistent with relativistic (nonrelativistic) canonical noncommutative spaces. In either case we obtain deformed generators, containing arbitrary free parameters, which close to yield new algebraic structures. We show that a particular choice of these parameters reproduces the undeformed algebra. The modified coproduct rules and the associated Hopf algebra are also obtained. Finally, we show that for the choice of parameters leading to the undeformed algebra, the deformations are represented by twist functions.