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Matrix canonical realizations of the Lie algebra o(m,n): I: Basic formulae and classification. (English) Zbl 0365.17004

MSC:
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
22E70 Applications of Lie groups to the sciences; explicit representations
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References:
[1] M. Havlicek and P. Exner , On the minimal canonical realizations of the Lie algebra OC(n) . Ann. Inst. H. Poincaré , t. 23 , Sect. A, n^\circ 4 , 1975 , p. 311 . Numdam | Zbl 0325.17001 · Zbl 0325.17001 · eudml:75878
[2] A. Joseph , Commun. math. Phys. , t. 36 , 1974 , p. 325 . Article | MR 342049 | Zbl 0285.17007 · Zbl 0285.17007 · doi:10.1007/BF01646204 · minidml.mathdoc.fr
[3] J.L. Richard , Ann. Inst. H. Poincaré , t. 8 , Sect. A, n^\circ 3 , 1968 , p. 301 . Numdam | Zbl 0161.23705 · Zbl 0161.23705 · numdam:AIHPA_1968__8_3_301_0 · eudml:75594
[4] A. Joseph , J. Math. Phys. , t. 13 , 1972 , p. 351 . Zbl 0238.17004 · Zbl 0238.17004 · doi:10.1063/1.1665983
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[8] E. Nelson , Ann. Math. , t. 70 , n^\circ 3 , 1959 , p. 572 . J. Simon , Commun. math. Phys. , t. 28 , 1972 , p. 39 . M. Havlicek , Remark on the integrability of some representations of the semi-simple Lie algebras . Rep. Math. Phys. , to appear. MR 107176 | Zbl 0091.10704 · Zbl 0091.10704 · doi:10.2307/1970331
[9] H.D. Doebner and O. Melsheimer , Nuovo Cim. , Ser. 10 , t. 49 , 1967 , p. 73 . MR 213110 | Zbl 0163.22504 · Zbl 0163.22504 · doi:10.1007/BF02739076
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