Remarks on Yangian-type algebras and double Poisson brackets
Representation Theory
2024-05-08 v1 Mathematical Physics
math.MP
Quantum Algebra
Rings and Algebras
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.
Keywords
Cite
@article{arxiv.2308.13325,
title = {Remarks on Yangian-type algebras and double Poisson brackets},
author = {Grigori Olshanski and Nikita Safonkin},
journal= {arXiv preprint arXiv:2308.13325},
year = {2024}
}