# Higher-order Galilean contractions

## TL;DR

This paper generalizes Galilean contractions to multiple conformal algebras, creating higher-order Galilean conformal algebras, with detailed examples including Virasoro, Kac-Moody, and W3 algebras.

## Contribution

It introduces a new method to construct higher-order Galilean conformal algebras from multiple inputs, expanding the algebraic framework.

## Key findings

- Constructed higher-order Galilean Virasoro algebras
- Developed higher-order Galilean Kac-Moody and W3 algebras
- Provided explicit examples and hierarchical structures

## Abstract

A Galilean contraction is a way to construct Galilean conformal algebras from a pair of infinite-dimensional conformal algebras, or equivalently, a method for contracting tensor products of vertex algebras. Here, we present a generalisation of the Galilean contraction prescription to allow for inputs of any finite number of conformal algebras, resulting in new classes of higher-order Galilean conformal algebras. We provide several detailed examples, including infinite hierarchies of higher-order Galilean Virasoro algebras, affine Kac-Moody algebras and the associated Sugawara constructions, and $W_{3}$ algebras.