Generalized Yangians and their Poisson counterparts

By generalized Yangians, we mean Yangian-like algebras of two different classes. One class comprises the previously introduced so-called braided Yangians. Braided Yangians have properties similar to those of the reflection equation algebra. Generalized Yangians of the second class, $RTT$-type Yangians, are defined by the same formulas as the usual Yangians but with other quantum $R$-matrices. If such an $R$-matrix is the simplest trigonometric $R$-matrix, then the corresponding $RTT$-type Yangian is called a $q$-Yangian. We claim that each generalized Yangian is a deformation of the commutative algebra $\operatorname{Sym}(gl(m)[t^{-1}])$ if the corresponding $R$-matrix is a deformation of the flip operator. We give the explicit form of the corresponding Poisson brackets.