# N=4 l-conformal Galilei superalgebra

## TL;DR

This paper constructs an N=4 supersymmetric extension of the l-conformal Galilei algebra by combining spatial symmetry generators with a superconformal group, resulting in a finite-dimensional superalgebra with specific parameter constraints.

## Contribution

It introduces a new N=4 superalgebra by integrating the l-conformal Galilei algebra with a superconformal group, fixing the group parameter for finiteness.

## Key findings

- Superalgebra constructed with fixed parameter a=-1/2
- Reduction of D(2,1;a) to OSp(4|2)
- Finite-dimensional N=4 superalgebra achieved

## Abstract

An N=4 supersymmetric extension of the l-conformal Galilei algebra is constructed. This is achieved by combining generators of spatial symmetries from the l-conformal Galilei algebra and those underlying the most general superconformal group in one dimension D(2,1;a). The value of the group parameter a is fixed from the requirement that the resulting superalgebra is finite-dimensional. The analysis reveals a=-1/2 thus reducing D(2,1;a) to OSp(4|2).