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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Dedicated to the memory of P. P. Kulish
Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 192, No. 3, pp. 351–368, September, 2017.
The research of P. A. Saponov was supported by the Russian Academic Excellence Project 5-100 and in part by the Russian Foundation for Basic Research (Grant No. 16-01-00562).
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Gurevich, D.I., Saponov, P.A. Generalized Yangians and their Poisson counterparts. Theor Math Phys 192, 1243–1257 (2017). https://doi.org/10.1134/S004057791709001X
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DOI: https://doi.org/10.1134/S004057791709001X