On affine yangians
On affine yangians
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关于仿射杨吉斯
DOI：
10.1007/bf00761137
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发表时间：
1994
影响因子：
1.2
通讯作者：
S. Levendorskii
中科院分区：
文献类型：
--
作者：
S. Boyarchenko;S. Levendorskii
构造了二维循环代数sl(2)⊗C[t−1，t；u]的泛包络代数的形变--杨安。这种形变类似于V.Drinfeld为任何简单李代数构造的杨安。证明了的PBW定理，并构造了一些表示。像通常的延安人一样，拥有一维自同构群和零能级-二维自同构群。这一观察结果允许人们猜测，的表示理论应该引起QYBE的新的解。其他仿射代数的延安可以类似地构造，它们具有相似的性质。
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 foris 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 ofshould give rise to new solutions of QYBE.Yangians of other affine algebras can be constructed similarly and they enjoy similar properties.