# Extended $D=3$ Bargmann supergravity from a Lie algebra expansion

## TL;DR

This paper demonstrates how Lie algebra expansion can systematically derive the extended Bargmann superalgebra and its Chern-Simons action in three dimensions from superPoincaré supergravity, simplifying the construction process.

## Contribution

It introduces a straightforward method to obtain extended Bargmann superalgebras and their Chern-Simons actions from superPoincaré algebra using Lie algebra expansions.

## Key findings

- Derived extended Bargmann superalgebra from superPoincaré algebra.
- Constructed Chern-Simons action for the extended Bargmann superalgebra.
- Simplified the process of obtaining non-relativistic supergravity models.

## Abstract

In this paper we show how the method of Lie algebra expansions may be used to obtain, in a simple way, both the extended Bargmann Lie superalgebra and the Chern-Simons action associated to it in three dimensions, starting from $D=3$, $\mathcal{N}=2$ superPoincar\'e and its corresponding Chern-Simons supergravity.