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Generalized Yangians and their Poisson counterparts
Theoretical and Mathematical Physics. 2017. Vol. 192. No. 3. P. 1243–1257.
Gurevich D. I., P.A. Saponov
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, RT T -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 RT T -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.
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