Braided Matrix Structure of $q$-Minkowski Space and $q$-Poincare Group

TL;DR

This paper explores the algebraic structure of q-Minkowski space and q-Poincare group, clarifying their relations and introducing new R-matrix formulas within a braided matrix framework.

Contribution

It establishes a connection between existing q-Minkowski space approaches and a braided Hermitean matrix framework, providing new R-matrix formulas for the q-Poincare group.

Findings

Unified the approach to q-Minkowski space

Derived new R-matrix formulas for q-Poincare group

Revealed braid statistics in matrix structures

Abstract

We clarify the relation between the approach to $q$-Minkowski space of Carow-Watamura et al. with an approach based on the idea of $2\times 2$ braided Hermitean matrices. The latter are objects like super-matrices but with Bose-Fermi statistics replaced by braid statistics. We also obtain new R-matrix formulae for the $q$-Poincare group in this framework.