# Generalized Yangians and their Poisson counterparts

## TL;DR

This paper introduces generalized Yangians, including braided and RTT-type, and explores their structure as deformations of symmetric algebras along with their associated Poisson brackets.

## Contribution

It defines two classes of generalized Yangians, establishes their deformation properties, and derives their Poisson structures, extending the theory of Yangians.

## Key findings

- Generalized Yangians are deformations of symmetric algebras.
- Poisson brackets corresponding to these Yangians are explicitly described.
- Braided and RTT-type Yangians are unified under a common deformation framework.

## Abstract

By a generalized Yangian we mean a Yangian-like algebra of one of two classes. One of these classes consists of the so-called braided Yangians, introduced in our previous paper. The braided Yangians are in a sense similar to the reflection equation algebra. The generalized Yangians of second class, called the Yangians of RTT type, are defined by the same formulae as the usual Yangians are but with other quantum $R$-matrices. If such an $R$-matrix is the simplest trigonometrical $R$-matrix, the corresponding Yangian of RTT type is the so-called q-Yangian. We claim that each generalized Yangian is a deformation of the commutative algebra ${\rm Sym}(gl(m)[t^{-1}])$ provided that the corresponding $R$-matrix is a deformation of the flip. Also, we exhibit the corresponding Poisson brackets.