# Dynkin automorphisms actions on Gaudin algebras

**Authors:** Vladyslav Zveryk  
**arXiv:** [2311.11872](https://arxiv.org/abs/2311.11872)  
**Date:** 2023-11-20  
**Summary page:** https://www.summarizepaper.com/fr/paper/2311.11872v1/

## Abstract

In this paper, we study the action of a Dynkin automorphism $\sigma$ of a simple Lie algebra $\mathfrak{g}$ on the generalized Gaudin algebras. In particular, we show isomorphisms between the coinvariants of the generalized Gaudin algebras associated with $\mathrm{Lie}(\mathfrak{g}^\vee)$ and the generalized Gaudin algebras associated with $\mathrm{Lie}(\mathfrak{g}_\sigma^\vee)$, where $\mathfrak{g}_\sigma$ is the fixed point subalgebra.