Geodesic
Generalized Yangians and their Poisson counterparts
Teoretičeskaâ i matematičeskaâ fizika, Tome 192 (2017) no. 3, pp. 351-368

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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 $\operatorname{Sym}(gl(m)[t^{-1}])$ if the corresponding $R$-matrix is a deformation of the flip operator. We give the explicit form of the corresponding Poisson brackets.
Mots-clés : current $R$-matrix, Poisson structure
Keywords: braided Yangian, quantum symmetric polynomial, quantum determinant, deformation property. 
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     author = {D. I. Gurevich and P. A. Saponov},
     title = {Generalized {Yangians} and their {Poisson} counterparts},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {192},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_192_3_a0/}
}
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D. I. Gurevich; P. A. Saponov. Generalized Yangians and their Poisson counterparts. Teoretičeskaâ i matematičeskaâ fizika, Tome 192 (2017) no. 3, pp. 351-368. http://geodesic.mathdoc.fr/item/TMF_2017_192_3_a0/