Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach

TL;DR

This paper introduces new Abelian twists of the Poincare algebra to construct Lie-deformed quantum Minkowski spaces, comparing Hopf-algebraic and Hopf-algebroid approaches to quantum symmetries and phase spaces.

Contribution

It develops new Abelian twists leading to Lie-deformed quantum Minkowski spaces and compares two quantization methods: Hopf-algebraic and Hopf-algebroid frameworks.

Findings

Constructed new Abelian twists for Poincare algebra.

Derived quantum Poincare-Hopf algebras with deformed symmetries.

Embedded generalized phase spaces into quantum-deformed Heisenberg algebras.

Abstract

We consider new Abelian twists of Poincare algebra describing non-symmetric generalization of the ones given in [1], which lead to the class of Lie-deformed quantum Minkowski spaces. We apply corresponding twist quantization in two ways: as generating quantum Poincare-Hopf algebra providing quantum Poincare symmetries, and by considering the quantization which provides Hopf algebroid describing the class of quantum relativistic phase spaces with built-in quantum Poincare covariance. If we assume that Lorentz generators are orbital i.e.do not describe spin degrees of freedom, one can embed the considered generalized phase spaces into the ones describing the quantum-deformed Heisenberg algebras.