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Some Lie Admissible Algebras

Published online by Cambridge University Press:  20 November 2018

P. J. Laufer  and
M. L. Tomber
P. J. Laufer
Affiliation:
College Militaire Royal de St-Jean
M. L. Tomber
Affiliation:
Michigan State University
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Several studies have been made to obtain larger classes of non-associative algebras from classes of algebras with a known structure. Thus, we have right alternative algebras (2)* and non-commutative Jordan algebras (6), (7), (8), and (9). These algebras are defined by a subset of the set of identities of the algebras from which they derive their names. Also, Albert (1), among others has studied Jordan admissible algebras. This paper is concerned with algebras which are related to Lie algebras in that they satisfy some of the identities of a Lie algebra and are Lie admissible. Theorem 2 answers a question raised by Albert in (1).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 14 , 1962 , pp. 287 - 292
Copyright
Copyright © Canadian Mathematical Society 1962

References

1. Albert, A. A., Power-associative rings, Trans. Amer. Math. Soc, 64 (1948), 552–593.Google Scholar
2. Albert, A. A., On right alternative algebras, Ann. Math., 50 (1949), 318–328.Google Scholar
3. Cartan, E., Sur la structure des groupes de transformations finis et continus, OEuvres Complètes (Paris, 1950) vol. I, part I, 137–287.Google Scholar
4. Dynkin, E. B., The structure of semi-simple algebras, Amer. Math. Soc. Translations No. 17 (1950).Google Scholar
5. Kleinfeld, E., Alternative and right alternative rings, Linear algebras, Nat. Acad. Sci. Pub. 502 (1957).Google Scholar
6. Kokoris, L. A., Some nodal noncommutative Jordan algebras, Proc. Amer. Math. Soc, 9 (1958), 164–166.Google Scholar
7. Schafer, R. D., Noncommutative Jordan algebras of characteristic 0, Proc. Amer. Math. Soc, 6 (1955), 472–475.Google Scholar
8. Schafer, R. D., On noncommutative Jordan algebras, Proc. Amer. Math. Soc, 9 (1958), 110–117.Google Scholar
9. Schafer, R. D., Restricted noncommutative Jordan algebras of characteristic p, Proc. Amer. Math. Soc, 9 (1958), 141–144.Google Scholar
10. Weiner, L. M., Lie admissible algebras, Univ. Nac Tucumân Rev. Ser. A., 11 (1957), 10–24.Google Scholar
11. Weyl, H., The structure and representation of continuous groups, The Institute for Advanced Study (1935).Google Scholar