Existence and conjugacy of Cartan subalgebras of Jordan algebras
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- by Ottmar Loos
- Proc. Amer. Math. Soc. 50 (1975), 40-44
- DOI: https://doi.org/10.1090/S0002-9939-1975-0369460-4
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Abstract:
It is shown that a finite-dimensional Jordan algebra over a field $k$ of characteristic $\ne 2$ contains Cartan subalgebras, and that any two Cartan subalgebras are conjugate by an inner automorphism provided $k$ is algebraically closed.References
- Armand Borel, Linear algebraic groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Notes taken by Hyman Bass. MR 0251042
- D. M. Foster, Generalizations of nilpotence and solvability in universal classes of algebras, J. Algebra 26 (1973), 536–555. MR 332900, DOI 10.1016/0021-8693(73)90013-6
- Nathan Jacobson, Structure and representations of Jordan algebras, American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, R.I., 1968. MR 0251099
- Ottmar Loos, Jordan pairs, Lecture Notes in Mathematics, Vol. 460, Springer-Verlag, Berlin-New York, 1975. MR 0444721
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 50 (1975), 40-44
- MSC: Primary 17C10
- DOI: https://doi.org/10.1090/S0002-9939-1975-0369460-4
- MathSciNet review: 0369460