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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.
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Submitted on : Thursday, March 18, 2021 - 10:11:38 AM
Last modification on : Thursday, September 8, 2022 - 3:57:57 PM

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Dimitri Gurevich, Pavel Saponov. Generalized Yangians and their Poisson counterparts. Theoretical and Mathematical Physics, Consultants bureau, 2017, 192 (3), pp.1243 - 1257. ⟨10.1134/S004057791709001X⟩. ⟨hal-03172948⟩

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