The Geometry of Jordan and Lie Structures - Lecture Notes in Mathematics - Wolfgang Bertram - 書籍 - Springer-Verlag Berlin and Heidelberg Gm - 9783540414261 - 2000年12月12日
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Wolfgang Bertram
The Geometry of Jordan and Lie Structures - Lecture Notes in Mathematics 2000 edition

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0. In this work of we the Lie- and Jordan on an study interplay theory and ona level. Weintendtocontinue ittoa algebraic geometric systematicstudy ofthe role Jordan inharmonic In the of theoryplays analysis. fact, applications the of Jordan to theharmonic on cones theory algebras analysis symmetric (cf. of the wereatthe theauthor'sworkinthisarea. Then monograph[FK94]) origin Jordan in of turned the causal algebras up study many symmetric (see spaces Section and clearthat all soon itbecame XI.3), "generically" symmetric spaces have Since a relation toJordan Jordan does not significant theory. theory (yet) to the standard tools inharmonic the is text belong analysis, present designed to self-contained introduction to Jordan for readers a provide theory having basic Lie and Our ofview some on knowledge groups symmetric spaces. point is introduce first the relevant structures geometric: throughout we geometric anddeducefromtheir identities fortheassociated propertiesalgebraic algebraic structures. Thus our differs from related ones presentation (cf. e. g. [FK94], the fact thatwe do not take an axiomatic definition ofsome [Lo77], [Sa80]) by Jordan structureasour Let us nowanoverviewof algebraic startingpoint. give the See alsothe introductions the contents. at ofeach given beginning chapter. 0.1. Lie and Jordan Ifwe the associative algebras algebras. decompose of the matrix in its and product algebra M(n, R) symmetric skew-symmetric parts, - XY YX XY YX + XY= + (0.1) 2 2 then second the term leads to the Lie with algebra gf(n, R) product [X, Y] XY- and first the termleadstotheJordan M with YX, algebra (n, R) product - X Y= + (XY YX).

274 pages, biography

メディア 書籍     Paperback Book   (ソフトカバーで背表紙を接着した本)
リリース済み 2000年12月12日
ISBN13 9783540414261
出版社 Springer-Verlag Berlin and Heidelberg Gm
ページ数 274
寸法 156 × 234 × 15 mm   ·   412 g
言語 英語   フランス語  

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