Abstract
Two new constructions of prime Jordan algebras containing nonzero trivial elements are presented. It is proved that a Jordan superalgebra of Poisson brackets is a homomorphic image of a special one.
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References
S. V. Pchelintsev, “Prime algebras and nonzero trivial elements,”Izv. Akad. Nauk SSSR, Ser. Mat.,50, No. 1, 79–100 (1986).
Yu. A. Medvedev and E. I. Zelmanov,Some Counter-examples in the Theory of Jordan Algebras, Preprint of the University of Virginia, Charlottesville, 1990.
I. P. Shestakov, “Superalgebras and counter-examples,”Sib. Mat. Zh.,32, No. 6, 187–196 (1991).
I. L. Kantor,Connection between Poisson Brackets and Jordan and Lie Superalgebras, Preprint Universite de Montreal, Canada (1989).
D. King and K. McCrimmon, “The Kantor construction of Jordan superalgebras,Commun. Algebra,20, No. 1, 109–126 (1992).
M. Scheunert, “The theory of Lie superalgebras,”Lecture Notes Math., 716, Springer-Verlag, Berlin (1979).
Additional information
Translated fromAlgebra i Logika, Vol. 33, No. 3, pp. 301–316, May–June, 1994.
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Skosyrskii, V.G. Prime Jordan algebras and the Kantor construction. Algebr Logic 33, 169–179 (1994). https://doi.org/10.1007/BF00750232
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DOI: https://doi.org/10.1007/BF00750232