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Generalised Yangians and their Poisson counterparts

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Dimitri Gurevich
Valenciennes University
Tue, 2017-03-14 14:00 - 15:00
MPIM Lecture Hall

By a generalized Yangian I mean a Yangian-like algebra of one of two classes. One of
them consists  of the so-called braided Yangians, recently introduced by myself and
Pavel Saponov. 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. In my talk I plan to present a comparative analyse of the generalized
Yangians and to exhibit the Poisson structures corresponding to the generalized Yangians which
are deformations of  commutative algebras.

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