Maximal Abelian subgroups of the isometry and conformal groups of Euclidean and Minkowski spaces
Maximal Abelian subgroups of the isometry and conformal groups of Euclidean and Minkowski spaces
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欧几里得空间和闵可夫斯基空间的等距群和共形群的最大阿贝尔子群
DOI：
10.1088/0305-4470/31/7/016
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
P. Winternitz
中科院分区：
文献类型：
--
作者：
Z. Thomova;P. Winternitz
欧氏李代数和伪欧氏李代数的极大阿贝尔子代数(MAS)分别在相应的李群和作用下以及在保形群和作用下被分成共轭类。结果以分解定理的形式给出。对于p=1和p=2时，只有当p=1和p=2时，才存在正交不可分解的MAS.另一方面，对于p的所有值，都存在正交不可分解的MAS.结果被用来构造新的坐标系，其中波动方程和Hamilton-Jacobi方程允许分离变量.
The maximal Abelian subalgebras (MASAs) of the Euclidean and pseudo-euclidean Lie algebras are classified into conjugacy classes under the action of the corresponding Lie groups and , and also under the conformal groups and , respectively. The results are presented in terms of decomposition theorems. For orthogonally indecomposable MASAs exist only for p = 1 and p = 2. For , on the other hand, orthogonally indecomposable MASAs exist for all values of p. The results are used to construct new coordinate systems in which wave equations and Hamilton-Jacobi equations allow the separation of variables.