K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist

TL;DR

This paper constructs a unified framework for k-Poincare algebra and k-Minkowski spacetime using twist deformation of Hopf algebroid structures in quantum phase space, facilitating noncommutative spacetime physics.

Contribution

It explicitly constructs k-Poincare-Hopf algebra and k-Minkowski spacetime from twist, extending to super algebra, and links these to noncommutative spacetime theories.

Findings

Explicit construction of k-Poincare-Hopf algebra from twist

Development of k-deformed phase space with Hopf algebroid structure

Extension to k-deformed super algebra including exterior forms

Abstract

We unify k-Poincare algebra and k-Minkowski spacetime by embeding them into quantum phase space. The quantum phase space has Hopf algebroid structure to which we apply the twist in order to get k- deformed Hopf algebroid structure and k-deformed phase space. We explicitly construct k-Poincare-Hopf algebra and k-Minkowski spacetime from twist. It is outlined how this construction can be extended to k-deformed super algebra including exterior derivative and forms. Our results are relevant for constructing physical theories on noncommutative spacetime by twisting Hopf algebroid phase space structure.