Abstract

Let A be an arbitrary associative algebra. With the help of Olshanski’s centralizer construction one can define a sequence Y_1(A), Y_2(A),... of "Yangian-type algebras" (they possess a number of properties of the Yangians of series A). I will discuss a link between these Yangian-type algebras and a class of double Poisson brackets on free associative algebras. The talk is based on the joint paper with Grigori Olshanski arXiv:2308.13325.