Nonlinear deformations of su(2) and su(1,1) generalizing Witten's algebra
Nonlinear deformations of su(2) and su(1,1) generalizing Witten's algebra
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DOI：
10.1088/0305-4470/26/4/001
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发表时间：
1993-02
期刊：
影响因子：
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通讯作者：
C. Delbecq;C. Quesne
中科院分区：
文献类型：
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作者：
C. Delbecq;C. Quesne
考虑了su（2）和su（1，1）涉及两个变形函数f（J 0）和g（J 0）的非线性变形.当g（J 0）=1时，它们化为一些最早由Polychronakos（1990）和Rocek（1991）研究的代数。空间重点放在g（J 0）是J 0的线性函数的情况下。结果表明，对于任意λ = 2，3，. . .,存在分别是su（2）或su（1，1）的变形的（λ-1）-参数代数，并且f（J 0）是λ次多项式.当λ =2时，这样的代数等价于维滕（1990）对su（2）或su（1，1）的第一变形。对于任何λ，J 0的谱是指数的，而不是g（J 0）=1的情况下的线性。
Nonlinear deformations of su(2) and su(1,1) involving two deforming functions f(J0) and g(J0) are considered. For g(J0)=1, they reduce to some algebras first studied by Polychronakos (1990) and Rocek (1991). Spatial emphasis is laid on the case where g(J0) is a linear function of J0. It is shown that for any lambda =2,3,. . ., there exist ( lambda -1)-parameter algebras that are deformations of su(2) or su(1,1) respectively, and for which f(J0) is a polynomial of degree lambda . For lambda =2, such algebras are equivalent to Witten's (1990) first deformation of su(2) or su(1,1). For any lambda , the spectrum of J0 is exponential instead of linear as in the case where g(J0)=1.