Representations of Jordan triples

Loos, Ottmar

doi:10.1090/S0002-9947-1973-0327857-5

Representations of Jordan triples
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by Ottmar Loos

Trans. Amer. Math. Soc. 185 (1973), 199-211

DOI: https://doi.org/10.1090/S0002-9947-1973-0327857-5

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Abstract:

Some standard results on representations of quadratic Jordan algebras are extended to Jordan triples. It is shown that the universal envelope of a finite-dimensional Jordan triple is finite-dimensional, and that it is nilpotent if the Jordan triple is radical. A permanence principle and a duality principle are proved which are useful in deriving identities.

References

N. Jacobson, Lectures on quadratic Jordan algebras, Tata Institute of Fundamental Research Lectures on Mathematics, No. 45, Tata Institute of Fundamental Research, Bombay, 1969. MR 0325715
Ottmar Loos, Lectures on Jordan triples, University of British Columbia, Vancouver, B.C., 1971. MR 0325717

On algebraic groups defined by Jordan structures

Kevin McCrimmon, Representations of quadratic Jordan algebras, Trans. Amer. Math. Soc. 153 (1971), 279–305. MR 268240, DOI 10.1090/S0002-9947-1971-0268240-9
Kurt Meyberg, Lectures on algebras and triple systems, University of Virginia, Charlottesville, Va., 1972. Notes on a course of lectures given during the academic year 1971–1972. MR 0340353
Kiyosi Yamaguti, On representations of Jordan triple systems, Kumamoto J. Sci. Ser. A 5 (1962), 171–184 (1962). MR 153716