Abstract
In joint work with Alain D’Amour, we have simplified and quadratified Zelmanov’s characterization of prime Jordan triples and pairs. A key tool in our work is Loos’ theory of the socle. Using Meyberg’s local algebra, we can carry Anquela, Cortes, and Montaner’s result that a primitive PI algebra has a nonzero socle back to primitive triples and pairs. This technique of using local algebras to pass information back and forth between systems and algebras is an important one, and we want to propagandize on its behalf.
This research was partially supported by NSF Grant DMS-8903309.
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References
J. Anquela, T. Cortes, F. Montaner: The structure of primitive quadratic Jordan algebras,to appear in J. Alg.
A. D’Amour and K. McCrimmon: Local algebras of Jordan systems,to appear.
O. Loos: Jordan Pairs, Lecture Notes in Math. vol. 460, Springer-Verlag, Berlin- Heidelberg-New York (1975).
O. Loos: On the socle of a Jordan pair, Collect. Math. 40 (1989), 109–125.
O. Loos and E. Neher: Complementation of inner ideals in Jordan pairs,to appear in J. Alg.
K. Meyberg: Lectures on algebras and triple systems, Lecture Notes, University of Virginia, Charlottesville (1972).
E. Zelmanov: Prime Jordan triple systems I,II,III, Siberian Math. J. 24 (1983), 23–37; 25 (1984), 50–61; 26 (1985), 71–82.
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© 1994 Springer Science+Business Media Dordrecht
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McCrimmon, K. (1994). Local Algebras. In: González, S. (eds) Non-Associative Algebra and Its Applications. Mathematics and Its Applications, vol 303. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0990-1_46
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DOI: https://doi.org/10.1007/978-94-011-0990-1_46
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