Lie-admissible, nodal, noncommutative Jordan algebras
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- by D. R. Scribner PDF
- Trans. Amer. Math. Soc. 154 (1971), 105-111 Request permission
Abstract:
The main theorem is that if A is a central simple flexible algebra, with an identity, of arbitrary dimension over a field F of characteristic not 2, and if A is Lie-admissible and ${A^ + }$ is associative, then ${\text {ad}}\;(A)’ = [A,A]/F$ is a simple Lie algebra. It is shown that this theorem applies to simple nodal noncommutative Jordan algebras of arbitrary dimension, and hence that such an algebra A also has derived algebra ${\text {ad}}\;(A)’$ simple.References
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- Robert H. Oehmke, Nodal noncommutative Jordan algebras, Trans. Amer. Math. Soc. 112 (1964), 416–431. MR 179220, DOI 10.1090/S0002-9947-1964-0179220-2
- T. S. Ravisankar, A note on a theorem of Kokoris, Proc. Amer. Math. Soc. 21 (1969), 355–356. MR 238911, DOI 10.1090/S0002-9939-1969-0238911-5
- Richard D. Schafer, An introduction to nonassociative algebras, Pure and Applied Mathematics, Vol. 22, Academic Press, New York-London, 1966. MR 0210757
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 154 (1971), 105-111
- MSC: Primary 17A15
- DOI: https://doi.org/10.1090/S0002-9947-1971-0314919-X
- MathSciNet review: 0314919