Kappa-Deformations: Historical Developments and Recent Results

TL;DR

This paper reviews the historical development of $ppa$-deformations, their influence on Doubly Special Relativity, and recent advances in describing quantum-covariant phase spaces and superstring target spaces using $ppa$-deformations.

Contribution

It provides a comprehensive overview of $ppa$-deformations, highlighting recent progress in their mathematical description and applications to superstring theory.

Findings

Description of quantum-covariant $ppa$-deformed phase spaces via Hopf algebroids

Analysis of $ppa$-deformations of $AdS_5 imes S^5$ superstring spaces

Historical connection between $ppa$-deformations and Doubly Special Relativity

Abstract

I shall recall in historical perspective some results from nineties and show further how $\kappa$-deformed symmetries and $\kappa$-Minkowski space inspired DSR (Doubly of Deformed Special Relativity) approach proposed after 2000. As very recent development I shall show how to describe quantum-covariant $\kappa$-deformed phase spaces by passing from Hopf algebras to Hopf algebroids (arXiv:1507.02612) and I will briefly describe the $\kappa$-deformations of $AdS_5 \times S^5$ superstring target spaces (arXiv:1510.030.83).