# N=4 l-conformal Galilei superalgebras inspired by D(2,1;a) supermultiplets

## TL;DR

This paper constructs N=4 supersymmetric extensions of the l-conformal Galilei algebra inspired by D(2,1;a) supermultiplets, revealing constraints on parameters and unifying previous models within a broader framework.

## Contribution

It introduces a general method to extend the l-conformal Galilei algebra using D(2,1;a) supermultiplets, clarifying parameter constraints and connecting to prior models.

## Key findings

- Jacobi identities constrain the parameter a for certain supermultiplets.
- The previously proposed N=4 l-conformal Galilei superalgebra is a special case of the new construction.
- The superalgebra structure depends on whether acceleration generators form irreducible or reducible supermultiplets.

## Abstract

N=4 supersymmetric extensions of the l-conformal Galilei algebra are constructed by properly extending the Lie superalgebra associated with the most general N=4 superconformal group in one dimension D(2,1;a). If the acceleration generators in the superalgebra form analogues of the irreducible (1,4,3)-, (2,4,2)-, (3,4,1)-, and (4,4,0)-supermultiplets of D(2,1;a), the parameter a turns out to be constrained by the Jacobi identities. In contrast, if the tower of the acceleration generators resembles a component decomposition of a generic real superfield, which is a reducible representation of D(2,1;a), a remains arbitrary. An N=4 l-conformal Galilei superalgebra recently proposed in [Phys. Lett. B 771 (2017) 401] is shown to be a particular instance of a more general construction in this work.