Hopf-algebra description of noncommutative-spacetime symmetries

TL;DR

This paper explores the symmetries of -Minkowski noncommutative spacetime using Hopf algebras, showing that a Poincare9-like symmetry can be constructed despite noncommutativity.

Contribution

It demonstrates how to describe -Minkowski spacetime symmetries with Hopf algebras, replacing traditional Lie algebra symmetries, and constructs an invariant action with a 10-generator Poincare9-like algebra.

Findings

Hopf algebra framework effectively describes noncommutative spacetime symmetries.

A 10-generator Poincare9-like algebra invariance is achievable in -Minkowski.

Traditional Lie algebra symmetries are replaced by Hopf algebra symmetries in noncommutative geometry.

Abstract

I give a brief summary of the results reported in hep-th 0306013 in collaboration with G. Amelino-Camelia and F. D'Andrea. I focus on the analysis of the symmetries of $\kappa$-Minkowski noncommutative space-time, described in terms of a Weyl map. The commutative space-time notion of Lie-algebra symmetries must be replaced by the one of Hopf-algebra symmetries. However, in the Hopf algebra sense, it is possible to construct an action in $\kappa$-Minkowski which is invariant under a 10-generators Poincar\'e-like symmetry algebra.