# Remarks on homogeneous solitons of the G$_2$-Laplacian flow

## TL;DR

This paper demonstrates the existence of specific expanding solitons in the G$_2$-Laplacian flow on non-solvable Lie groups and provides the first example of a steady soliton that is not extremally Ricci pinched.

## Contribution

It introduces new examples of solitons in the G$_2$-Laplacian flow, including the first non-extremally Ricci pinched steady soliton.

## Key findings

- Existence of expanding solitons on non-solvable Lie groups
- First example of a steady soliton not extremally Ricci pinched
- Advances understanding of G$_2$-Laplacian flow solutions

## Abstract

We show the existence of expanding solitons of the G$_2$-Laplacian flow on non-solvable Lie groups, and we give the first example of a steady soliton that is not an extremally Ricci pinched G$_2$-structure.