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On the Killing radical of Lie triple algebras. (English) Zbl 0521.17001

MSC:
17A40 Ternary compositions
17B30 Solvable, nilpotent (super)algebras
53C30 Differential geometry of homogeneous manifolds
17A65 Radical theory (nonassociative rings and algebras)
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[1] N. Bourbaki: Elements de Mathematique. Groupes et Algebres de Lie. Ch. 1, Algebre de Lie, Hermann (1960). · Zbl 0211.02401
[2] N. Jacobson: Lie Algebras. Interscience (1962). · Zbl 0121.27504
[3] M. Kikkawa: Geometry of homogeneous Lie loops. Hiroshima Math. J., 5, 141-179 (1975). · Zbl 0304.53037
[4] M. Kikkawa: a note on subloops of a homogeneous Lie loop and subsystems of its tangent Lie triple algebra, ibid., 5, 439-446 (1975). · Zbl 0312.53036
[5] M. Kikkawa: Triple systems on manifolds (homogeneous systems). Kokyuroku RIMS, Kyoto Univ., no. 308, 12-21 (1977).
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[11] O. Loos: Uber eine Beziehung zwischen Malcev-Algebren und Lie-Trippelsystemen. Pacific J. Math., 18, 553-562 (1966). · Zbl 0145.04202
[12] T. S. Ravisankar: On Malcev algebras, ibid., 42, 227-234 (1972). · Zbl 0245.17010
[13] T. S. Ravisankar: Some remarks on Lie triple systems. Kumamoto J. Sci. (Math.), 11, 1-8 (1974). · Zbl 0367.17006
[14] J. A. Wolf: On the geometry and classification of absolute parallelisms II. J. Diff. Geom., 7, 19-44 (1972). · Zbl 0276.53017
[15] K. Yamaguti: On the Lie triple systems and its generalization. J. Sci. Hiroshima Univ., Ser. A, 21, 155-160 (1957/1958). · Zbl 0084.18404
[16] K. Yamaguti: On the theory of Malcev algebras. Kumamoto J. Sci., Ser. A, 6, 9-45 (1963). · Zbl 0138.26203
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