Generalized Yangians and their Poisson counterparts

Abstract

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 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.