On affine yangians |
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| Authors: | S I Boyarchenko S Z Levendorskii |
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| Institution: | (1) Rostov Institute of Agriculture Machinery, Gagarin Sq. 1, 344010 Rostov-on-Don, Russia;(2) Rostov Institute of National Economy, Engels'a 69, 344798 Rostov-on-Don, Russia |
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| Abstract: | A Yangian
, a deformation of the universal enveloping algebra of the two-dimensional loop algebra sl(2)  C t
–1,t;u], is constructed. This deformation is an analogue of a Yangian which was constructed by V. Drinfeld for any simple Lie algebra. The PBW theorem for
is proved and some representations are constructed. Like usual Yangians,
possesses a one-dimensional group of auto- morphisms and at zero level - a two-dimensional group of automorphisms. This observation allows one to conjecture that the representation theory of
should give rise to new solutions of QYBE.Yangians of other affine algebras can be constructed similarly and they enjoy similar properties. |
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| Keywords: | 17B37 81R50 82B23 |
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