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Generalized Yangians and their Poisson counterparts by Gurevich, Dimitri; Saponov, Pavel is a scholarly article available to read on EtoBox.

What is Generalized Yangians and their Poisson counterparts about?

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.

Author

Gurevich, Dimitri; Saponov, Pavel

Published

2017

Language

EN