A Triangular Deformation of the two Dimensional Poincare Algebra

TL;DR

This paper introduces a new triangular deformation of the 2D Poincaré algebra derived from the $h$-deformation of SL(2,R), including explicit constructions of the R matrix and deformed structures.

Contribution

It presents a novel triangular deformation of the 2D Poincaré algebra with explicit universal R matrix and deformation map, expanding the understanding of quantum deformations.

Findings

Constructed a new triangular deformation of 2D Poincaré algebra.

Explicitly derived the universal R matrix for the deformation.

Presented deformed mass shells and Lorentz transformations.

Abstract

Contracting the $h$-deformation of $\SL(2,\Real)$, we construct a new deformation of two dimensional Poincar\'e algebra, the algebra of functions on its group and its differential structure. It is also shown that the Hopf algebra is triangular, and its universal R matrix is also constructed explicitly. Then, we find a deformation map for the universal enveloping algebra, and at the end, give the deformed mass shells and Lorentz transformation.