Abstract
In the first section we summarize some properties of Jordan triples. Then we state some rules about differential calculus of rational functions.
In the second section we generalize results about norms and traces of Jordan algebras.
In the next section we define a group of birational functions belonging to a Jordan triple and characterize this group by differential equations. A special form of these differential equations was given by M. Koecher (see [3], page 44, Theorem 2.1.).
In the last section we give some examples. In particular one obtains the exceptional group E6 as a homomorphic image of a transformation group.
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Literatur
Braun, H., Koecher, M.: Jordan-Algebren, Berlin-Heidelberg-New York: Springer 1966.
Jacobson, N.: Structure and representations of Jordan algebras, Amer. Math. Soc. Colloq. Publ., vol. 39: Amer. Math. Soc., Providence 1968.
Koecher, M.: An elementary approach to bounded symmetric domains, Houston,Texas: Rice University 1969.
Loos, O.: Lectures on Jordan triples, Lecture notes, Vancouver, British Columbia: University of British Columbia 1971.
Loos, O.: Jordan Pairs, Berlin-Heidelberg-New York: Springer 1975.
Meyberg, K.: Lectures on algebras and triple systems, Lecture notes, Charlottesville: University of Virginia 1973.
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Kühn, O. Differentialgleichungen in Jordantripelsystemen. Manuscripta Math 17, 363–381 (1975). https://doi.org/10.1007/BF01170732
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DOI: https://doi.org/10.1007/BF01170732