# Quantum Deformations of Relativistic Symmetries

## TL;DR

This paper explores quantum deformations of relativistic symmetries, specifically Lorentz and Poincare algebras, identifying how classical r-matrices relate to twisted deformations and providing explicit examples.

## Contribution

It classifies quantum deformations of D=4 Lorentz and Poincare algebras, linking Zakrzewski's r-matrices to specific twisted deformation types and providing explicit twist constructions.

## Key findings

- Most Zakrzewski r-matrices correspond to Abelian and Jordanian twists.
- Explicit forms of some twists are provided.
- The work enhances understanding of quantum symmetry deformations.

## Abstract

We discussed quantum deformations of D=4 Lorentz and Poincare algebras. In the case of Poincare algebra it is shown that almost all classical r-matrices of S. Zakrzewski classification correspond to twisted deformations of Abelian and Jordanian types. A part of twists corresponding to the r-matrices of Zakrzewski classification are given in explicit form.