Geodesic
Conjugacy of polar factorizations of Lie groups
Sbornik. Mathematics, Tome 13 (1971) no. 1, pp. 12-24 Cet article a éte moissonné depuis la source Math-Net.Ru

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A Lie group is said to be effective if it is connected and contains no compact normal divisors. A factorization of a connected Lie group into the product of two connected subgroups, the first of which is maximally compact and the second completely solvable is called a polar factorization. In this article the following theorem is proved. Theorem. Any two polar factorizations of an effective Lie group are conjugate under an inner automorphism. Bibliography: 5 titles. 
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D. V. Alekseevskii. Conjugacy of polar factorizations of Lie groups. Sbornik. Mathematics, Tome 13 (1971) no. 1, pp. 12-24. http://geodesic.mathdoc.fr/item/SM_1971_13_1_a1/

[1] Seminar “Sofus Li”, IL, Moskva, 1962

[2] I. Tits, “Automorphismes a deplacement borne de groupes de Lie”, Topology, 3:1 (1965), 97–107 | MR

[3] E. B. Vinberg, “Teorema Morozova–Borelya dlya veschestvennykh grupp Li”, DAN SSSR, 141:2 (1961), 270–274 | MR

[4] K. Shevalle, Teoriya grupp Li, t. 3, IL, Moskva, 1958

[5] A. Borel, Sous-groupes compacts maximaux des groupes de Lie, Seminaire Bourbaki, 33, 1950/51