Yangians of Classical Lie Superalgebras : Basic Constructions , Quantum Double and Universal R-Matrix
Yangians of Classical Lie Superalgebras : Basic Constructions , Quantum Double and Universal R-Matrix
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经典李超代数的杨量:基本结构,量子双态和通用R矩阵
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
V. Tolstoy
中科院分区：
文献类型：
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作者：
S. Khoroshkin;V. Tolstoy
描述了李超代数 Yangians 理论的一些基本结果。基本李超代数的杨量被描述为多项式环的李超代数的量化结果。此外，我们还考虑了扭曲电流的李超代数的量化。介绍了两个生成器系统和定义关系。证明了该生成元系统和定义关系的等价性。针对李超代数A(m,n)型Yangian，讨论了Yangian二重的概念和Yangian二重的通用R-矩阵公式。
Some basic results of the theory of Yangians of Lie superalgebras are described. Yangian of basic Lie superalgebra is described as a result of quantization of Lie superbialgebra of polynomial loops. Also, we consider a quantization of Lie superalgebra of twisted currents. Two systems of generators and defining relations are introduced. Equivalence of this systems of generators and defining relations is proved. The notion of double of Yangian and formula for universal R-matrix for double of Yangian are discussed for Yangian of Lie superalgebra A(m,n) type.