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Transactions of the American Mathematical Society

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Lie-admissible, nodal, noncommutative Jordan algebras


Author: D. R. Scribner
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
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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 [Enhancements On Off] (What's this?)

  • [1] I. N. Herstein, Topics in ring theory, Math. Lecture Notes, University of Chicago, 1965. MR 0271135 (42:6018)
  • [2] Kevin McCrimmon, Jordan algebras of degree 1, Bull. Amer. Math. Soc. 70 (1964), 702. MR 29 #2286. MR 0164995 (29:2286)
  • [3] Robert H. Oehmke, Nodal noncommutative Jordan algebras, Trans. Amer. Math. Soc. 112 (1964), 416-431. MR 31 #3469. MR 0179220 (31:3469)
  • [4] T. S. Ravisankar, A note on a theorem of Kokoris, Proc. Amer. Math. Soc. 21 (1969), 355-356. MR 39 #271. MR 0238911 (39:271)
  • [5] R. D. Schafer, An introduction to nonassociative algebras, Pure and Appl. Math., vol. 22, Academic Press, New York, 1966. MR 35 #1643. MR 0210757 (35:1643)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0314919-X
Keywords: Nodal algebras, noncommutative Jordan algebras, Lie-admissible algebras, infinite-dimensional algebras
Article copyright: © Copyright 1971 American Mathematical Society

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