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Faulkner, John R.

On the geometry of inner ideals. (English) Zbl 0285.17004

J. Algebra 26, 1-9 (1973).
Reviewer: James F. Hurley (Storrs)
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0285.17004

Cited in 3 Reviews
Cited in 29 Documents

MSC:

17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
17A40 Ternary compositions
51A25 Algebraization in linear incidence geometry

Citations:

Zbl 0224.17011; Zbl 0079.36203
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Full Text: DOI

References:

[1] Faulkner, J. R., A construction of Lie algebras from a class of ternary algebras, Trans. Amer. Math. Soc., 155, 397-408 (1971) · Zbl 0215.38503
[2] Faulkner, J. R., A geometry for \(E_7\), Trans. Amer. Math. Soc., 167, 49-58 (1972) · Zbl 0237.50004
[3] Jacobson, N., Lie and Jordan triple systems, Amer. J. Math., 71, 149-170 (1949) · Zbl 0034.16903
[4] Jacobson, N., Lie Algebras (1962), Interscience: Interscience New York · JFM 61.1044.02
[5] Lister, W. G., A structure theory of Lie triple systems, Trans. Amer. Math. Soc., 72, 217-242 (1952) · Zbl 0046.03404
[6] Meyberg, K., Jordan-Tripelsysteme und die Koecher-Konstruction von Lie-Algebren, Math. Z., 115, 58-78 (1970) · Zbl 0186.34501
[7] McCrimmon, K., Inner ideals in quadratic Jordan algebras, Trans. Amer. Math. Soc., 159, 445-468 (1971) · Zbl 0224.17011
[8] Schafer, R. D., An Introduction to Nonassociative Algebras (1966), Academic Press: Academic Press New York · Zbl 0145.25601
[9] Schellekens, G. J., On a hexagonic structure I, II, (Nederl. Akad. Wetensch. Proc. Ser. A, 65 (1962)), 201-234 · Zbl 0105.13001
[10] Springer, T. A.; Veldkamp, F. D., On Hjelmslev-Moufang planes, Math. Z., 107, 249-263 (1968) · Zbl 0164.51301
[11] Steinberg, K., Lectures on Chevalley groups, Yale University notes (1967)
[12] Tits, J., Groups semi-simples complexes et géométrie projective, (Séminaire Bourbaki (février 1955)) · Zbl 0117.37502
[13] Tits, J., Sur la géométrie des \(R\)-espaces, J. Math. Pures Appl., 36, 17-38 (1957) · Zbl 0079.36203
[14] Yamaguti, K., On algebras of totally geodesic spaces (Lie triple systems), J. Sci. Hiroshima Univ. Ser. A-1 Math., 21, 107-113 (1957/1958) · Zbl 0084.18405
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