Non-relativistic $k$-contractions of the Coadjoint Poincar\'e algebra

TL;DR

This paper explores non-relativistic k-contractions of the Poincaré algebra, extending it with central charges, and connects these to the coadjoint Poincaré algebra and p-brane Galilei algebra through specific quotients.

Contribution

It introduces a new class of k-contracted Poincaré algebra extensions and relates them to the coadjoint algebra and p-brane Galilei algebra.

Findings

Identification of new algebraic contractions

Connection to coadjoint Poincaré algebra

Recovery of p-brane Galilei algebra via quotients

Abstract

We study a class of extensions of the k-contracted Poincar\'e algebra under the hipotesis of generalizing the Bargmann algebra and his central charge. As we will see this type of contractions will lead in a natural way to consider the codajoint Poincar\'e algebra and some of their contractions. Among them there is one such that. considering the quotient of it by a suitable ideal, the (stringy) p-brane Galilei algebra is recovered.