Titlebook: Jordan Algebras and Algebraic Groups; Tonny A. Springer Book 1998 Springer-Verlag Berlin Heidelberg 1998 Area.Finite.Lie.Math.algebra.alge

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ation of Jordan algebras in the perspective of classification of certain root systems, the book demonstrates that the structure theories associative, Lie, and Jordan algebras are not separate creations but rather instances of the one all-encompassing miracle of root systems. ..." (Math. Reviews)978-3-540-63632-8978-3-642-61970-0

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Classification of Certain Algebraic Groups,he theory of linear algebraic groups which is basic for that classification. We shall have to rely heavily on the theory of semisimple algebraic groups and their rational representations, for which we refer to [10]. For the results on root systems to be used we refer to [7].

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J-structures,Let . be a finite dimensional vector space, let . be a rational map .. Denote by . and . a numerator and a denominator of ., respectively. . is a polynomial map of . into . and . a polynomial function on . (see 0.5). Let . be the subset of . × GL(.) consisting of the pairs (g, h) such that

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Examples,In this section we discuss some examples of J-structures. Almost all of them are related to associative algebras and quadratic forms.

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J-structures of Low Degree,We keep the notations of Section 4. In this section we shall discuss J-structures of degree . ≦ 3, the most interesting case being . = 3. The trivial case . 1 has already been discussed in 2.19.

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