Title: Generalized Yangians and their Poisson counterparts,
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.