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Wedderburnzerlegung für Jordan-Paare (1978)

Kühn, Oda ; Rosendahl, Adelheid

Springer

Manuscripta mathematica 24 (1978), S. 403-435

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ISSN: 1432-1785

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract In the first section we summarize some properties of Jordan pairs. Then we state some results about some groups defined by Jordan pairs. In the next section we construct a Lie algebra to a Jordan pair. This construction is a generalization of the wellknown “Koecher-Tits-construction”. We calculate the radical of this Lie algebra in terms of the given Jordan pair. In the last section we prove a Wedderburn decomposition theorem for Jordan pairs in the characteristic zero case. Some special cases in arbitrary characteristic have been shown by R. Carlson (see [5]). Also we show that any two such decompositions are conjugate under a certain group of automorphism. Analogous theorems will be shown for Jordan Triples.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01168884

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2

Electronic Resource

Differentialgleichungen in Jordantripelsystemen (1975)

Kühn, Oda

Springer

Manuscripta mathematica 17 (1975), S. 363-381

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ISSN: 1432-1785

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01170732

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