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A class of nonassociative algebras with involution containing the class of Jordan algebras. (English) Zbl 0368.17001


MSC:

17A30 Nonassociative algebras satisfying other identities
17A99 General nonassociative rings
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References:

[1] Allison, B.N.: A construction of Lie algebras from ?-ternary algebras. Amer. J. Math.98, 285-294 (1976) · Zbl 0342.17008 · doi:10.2307/2373884
[2] Bourbaki, N.: Lie groups and Lie algebras, Part I, Chapters 1-3. Reading: Addison Wesley 1975 · Zbl 0319.17002
[3] Faulkner, J.R.: A construction of Lie algebras from a class of ternary algebras. Trans. Amer. Soc.155, 397-408 (1971) · Zbl 0215.38503 · doi:10.1090/S0002-9947-1971-0294424-X
[4] Hein, W.: A construction of Lie algebras by triple systems. Trans. Amer. Math. Soc.205, 79-95 (1975) · Zbl 0306.17003 · doi:10.1090/S0002-9947-1975-0393153-5
[5] Jacobson, N.: Completely reducible Lie algebras of linear transformations. Proc. Amer. Math. Soc.2, 105-113 (1951) · Zbl 0043.26803 · doi:10.1090/S0002-9939-1951-0049882-5
[6] Jacobson, N.: Structure and representations of Jordan algebras. American Mathematical Society Colloquium Publications, Vol. 39. Providence, R.I.: American Mathematical Society, 1968 · Zbl 0218.17010
[7] Kantor, I.L.: Some generalizations of Jordan algebras. Trudy. Sem. Vektor Anal.16, 407-499 (1972), (Russian) · Zbl 0272.17001
[8] Kantor, I.L.: Models of exceptional Lie algebras. Soviet Math. Dokl.14, 254-258 (1973) · Zbl 0298.17009
[9] Koecher, M.: Imbedding of Jordan algebras into Lie algebras, I. Amer. J. Math.89, 787-815 (1967) · Zbl 0209.06801 · doi:10.2307/2373242
[10] Loos, K.: Über eine Beziehung zwischen Malcev-Algebren und Lie-Triplesystemen. Pacific J. Math.18, 553-562 (1966) · Zbl 0145.04202
[11] Meyberg, K.: Zur Konstruktion von Lie-Algebren aus Jordan-Triplesystemen. Manuscr. Math.3, 115-132 (1970) · Zbl 0211.35701 · doi:10.1007/BF01273306
[12] Meyberg, K.: Lectures on algebras and triple systems. University of Virginia Lecture Notes. Charlottesville 1972
[13] Sagle, A.: Malcev algebras. Trans. Amer. Math. Soc.101, 426-458 (1961) · Zbl 0101.02302 · doi:10.1090/S0002-9947-1961-0143791-X
[14] Schafer, R.: Introduction to nonassociative algebras. New York: Academic Press 1966 · Zbl 0145.25601
[15] Springer, T.A.: Characterization of a class of cubic forms. Nederl. Akad. Wetensch. Proc., Ser A65, 259-265 (1962) · Zbl 0108.03302
[16] Yamaguti, K.: On the metasymplectic geometry and ternary systems (to appear) · Zbl 0281.50015
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