Maximal abelian subalgebras of e(p, q) algebras

Linear Algebra and Its Applications

Volumn 291, Issue 1-3, 1999, Pages 245-274

  Thomova, Z ^a,b   Winternitz, P ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b SUNY POLYTECHNIC INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033442150     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(99)00006-3     Document Type: Article

References (24)

1. G. Frobenius, Über vertauschbare Matrizen, Sitzungsberichte der Kgl. Preussischen Akademie der Wissenschaften zu Berlin 8 (1896) 601-614.
2. I. Schur, Zur Theorie der vertauschbaren Matrizen, J. Reine Angew. Math. 130 (1905) 66-76.
3. M.F. Kravchuk, Über vertauschbare Matrizen, Rend. Circ. Math. Palermo 51 (1927) 126-130.
4. M. Gerstenhaber, Commuting matrices, Ann. of Math. 73 (1961) 324-348.
5. n, Duke Math. J. 32 (1965).
6. W.H. Gustafson, Maximal commutative algebras of linear transformations, J. Algebra 42 (1961) 557-563.
7. O. Taussky, Commutativity in finite matrices, Amer. Math. Monthly 64 (1957) 229-235.
8. T.J. Laffey, The minimal dimension of maximal commutative subalgebras of full matrix algebras, Linear Algebra Appl. 71 (1985) 199-212.
9. D.A. Suprunenko, R.I. Tyshkevich, Commutative Matrices, Academic Press, New York, 1968.
10. A.I. Maltsev, Commutative subalgebras of semi-simple Lie algebras, Izv. Akad. Nauk SSR Ser. Mat. 9 (1945) 291; Amer. Math. Soc. Transl. Ser. 1 9 (1962) 214.
11. A.I. Maltsev, Commutative subalgebras of semi-simple Lie algebras, Izv. Akad. Nauk SSR Ser. Mat. 9 (1945) 291; Amer. Math. Soc. Transl. Ser. 1 9 (1962) 214.
12. N. Jacobson, Lie Algebras, Dover, New York, 1979.
13. B. Kostant, On the conjugacy of real Cartan subalgebras I, Proc. Nat. Academy Sci. USA 41 (1955) 967-970.
14. M. Sugiura, Conjugate classes of Cartan subalgebras in real semi-simple algebras, J. Math. Soc. Japan 11 (1959) 374-434.
15. J. Patera, P. Winternitz, H. Zassenhaus, Maximal abelian subalgebras of real and complex symplectic Lie algebras, J. Math. Phys. 24 (1983) 1973-1985.
16. M.A. Olmo, H. Rodriguez, P. Winternitz, P. Zassenhaus, Maximal abelian subalgebras of pseudounitary Lie algebras, Linnear Algebra Appl. 135 (1990) 79-151.
17. V. Hussin, P. Winternitz, H. Zassenhaus, Maximal abelian subalgebras of complex orthogonal Lie algebras, Linnear Algebra Appl. 141 (1990) 183-220.
18. V. Hussin, P. Winternitz, H. Zassenhaus, Maximal abelian subalgebras of pseudoorthogonal Lie algebras, Linear Algebra Appl. 173 (1992) 125-163.
19. P. Winternitz, H. Zassenhaus, Decomposition theorems for maximal abelian subalgebras of the classical algebras, Report CRM-1199, 1984.
20. K.G. Kalnins, P. Winternitz, Maximal abelian subalgebras of complex euclidean Lie algebras, Can. J. Phys. 72 (1994) 389-404.
21. Z. Thomova, P. Winternitz, Maximal abelian subgroups of the isometry and conformal groups of Euclidean and Minkowski spaces, J. Phys. A 31 (1998) 1831-1858.
22. N. Burgoyne, R. Cushman, Conjugacy classes in linear groups, J. Algebra 44 (1977) 339-362.
23. A.I. Maltsev, Foundations of Linear Algebra, Freeman, San Francisco, 1963.
24. D.Z. Djokovic, J. Patera, P. Winternitz, H. Zassenhaus, Normal forms of elements of classical real and complex Lie and Jordan algebras, J. Math. Phys. 24 (1983) 1363-1374.