Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-14T23:08:21.202Z Has data issue: false hasContentIssue false
  • English
  • Français

Cartan Subalgebras of Jordan Algebras

Published online by Cambridge University Press:  22 January 2016

N. Jacobson
N. Jacobson*
Affiliation:
Yale University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we shall give a definition of an analogue for Jordan algebras of the classical notion of a Cartan subalgebra of a Lie algebra. This is based on a notion of associator nilpotency of a Jordan algebra. A Jordan algebra is called associator nilpotent if there exists a positive (odd) integer M such that every associator of order M formed of elements of is 0 (§2).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 591 - 609
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Albert, A. A., On Jordan algebras of linear transformations, Trans. Amer. Math. Soc, 59 (1946), 524–555.Google Scholar
[2] Albert, A. A., A structure theory for Jordan algebras, Ann. Math., 48 (1947), 546–567.Google Scholar
[3] Albert, A. A., A theory of power associative commutative algebras, Trans. Amer. Math. Soc, 69 (1950), 503–527.Google Scholar
[1] Chevalley, C., Théorie des groupes de Lie II (1951), III (1955), Act. Sci., Paris.Google Scholar
[1] Hochschild, G. P., On the algebraic hull of a Lie algebra, Proc. Amer. Math. Soc, 19 (1960), 195–200.CrossRefGoogle Scholar
[1] Jacobson, N., Derivation algebras and multiplication algebras of semi-simple Jordan algebras, Annals of Math., 50 (1949), 866–874.Google Scholar
[2] Jacobson, N., General representation theory of Jordan algebras, Trans. Amer. Math. Soc, 70 (1951), 509–530.CrossRefGoogle Scholar
[3] Jacobson, N., Structure of alternative and Jordan bimodules, Osaka Math. Jour., 6 (1954), 1–71.Google Scholar
[4] Jacobson, N., A theorem on the structure of Jordan algebras, Proc. Nat. Acad. Sci., 42 (1956), 140–147.Google Scholar
[5] Jacobson, N., Some groups of transformations defined by Jordan algebras I, Jour, für reine und angew. Math., 201 (1959), 178–195.Google Scholar
[6] Jacobson, N., Generic norm of an algebra, Osaka Math. Jour., 15 (1963), 25–50.Google Scholar
[1] McCrimmon, K., Jordan algebras of degree 1, Bull. Amer. Math. Soc, 70 (1964), p. 702.Google Scholar
[1] Penico, A. J., The Wedderburn principal theorem for Jordan algebras, Trans. Amer. Math., Soc, 70 (1951), 404–420.Google Scholar
[1] Tits, J., A theorem on generic norms of strictly power associative algebras, Proc. Amer. Math. Soc, 15 (1964), 35–36.Google Scholar