Remarks on Yangian-type algebras and double Poisson brackets

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.