Remarks on Yangian-type algebras and double Poisson brackets

TL;DR

This paper advances the study of Yangian-type algebras, expanding their construction and establishing a connection with linear double Poisson brackets, thus enriching the algebraic framework related to Yangians.

Contribution

It refines and enlarges the construction of Yangian-type algebras and links them to linear double Poisson brackets on free associative algebras.

Findings

Expanded construction of Yangian-type algebras

Established connection with linear double Poisson brackets

Enhanced understanding of algebraic properties of these structures

Abstract

This short note is an announcement of results. We continue the study of Yangian-type algebras initiated in the paper arXiv:2208.04809. These algebras share a number of properties of the Yangians of type A but are more massive. We refine and substantially enlarge the construction of that paper. A direct link with the class of linear double Poisson brackets on the free associative algebras (Pichereau and Van de Weyer, arXiv:math/0701837) is also established.