Quantum $\kappa$-Poincare in Any Dimensions

TL;DR

This paper develops a comprehensive framework for the $ppa$-deformation of D-dimensional Poincare9 algebras, deriving classical r-matrices and constructing the quantum Poincare9 group with noncommuting parameters for any signature.

Contribution

It provides the first explicit construction of the $ppa$-deformation for all D-dimensional Poincare9 algebras with arbitrary signature, including classical r-matrices and quantum group structures.

Findings

Derived quadratic Poisson brackets from classical r-matrices.

Constructed the quantum Poincare9 group with noncommuting parameters.

Extended $ppa$-deformation to any dimension and signature.

Abstract

The $\kappa$-deformation of the D-dimensional Poincar\'e algebra $(D\geq 2)$ with any signature is given. Further the quadratic Poisson brackets, determined by the classical $r$-matrix are calculated, and the quantum Poincar\'e group "with noncommuting parameters" is obtained.