Maximal Abelian Subgroups of the Isometry and Conformal Groups of Euclidean and Minkowski Spaces

Details 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

1997-07-04

arxiv.org/abs/physics/9707005v1

J.Phys.A31:1831-1858,1998

Physics

Mathematical Physics

31 pages, Latex (+ latexsym)

Scientific paper

10.1088/0305-4470/31/7/016

The maximal Abelian subalgebras of the Euclidean e(p,0) and pseudoeuclidean e(p,1)Lie algebras are classified into conjugacy classes under the action of the corresponding Lie groups E(p,0) and E(p,1), and also under the conformal groups O(p+1,1) and O(p+1,2), respectively. The results are presented in terms of decomposition theorems. For e(p,0) orthogonally indecomposable MASAs exist only for p=1 and p=2. For e(p,1), 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.

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