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Jordan-Algebren
$115.00
Description
Kommutative Algebren, in denen als Ersatz des Assoziativgesetzes 2 2 die Identitat (u v) u = u (v u) gilt, wurden erstmals von P. JORDAN im Jahre 1932 im Zusammenhang mit Fragen der Quantentheorie untersucht. Die Autoren P. JORDAN, J. VON NEUMANN und E. WIGNER gaben bald darauf eine Strukturtheorie der formal-reellen "Jordan Algebren". AnschlieBend waren die Jordan-Algebren Gegenstand zahl reicher rein algebraischer Untersuchungen. Man verdankt hier ins besondere A. A. ALBERT und N. JACOBSON interessante und tiefliegende Ergebnisse. Die Einzelheiten der Entwicklung der Theorie der Jordan Algebren kann man recht gut dem (von uns moglichst vollstandig angegebenen) Literaturverzeichnis entnehmen. Es sind darin auch die jenigen Publikationen aufgenommen worden, die sich nicht in den Rahmen des vorliegenden Buches einfligen. Dieses Literaturverzeichnis umfaBt die Publikationen fiber nicht-assoziative Algebren mit AusschluB der Lie-Algebren. Jordan-Algebren und alternative Algebren haben mehr noch als Lie-Algebren den AnstoB zum Studium allgemeiner nicht-assoziativer Algebren gegeben. In letzter Zeit ergaben sich neben neuen algebraischen Aspekten auch Anwendungen der Jordan-Algebren auf Teile der Analysis. Damit stehen die Jordan-Algebren erganzend neben den Lie-Algebren. Die Autoren gelangten zu den Jordan-Algebren, indem sie von Problem en der Analysis, genauer von der systematischen Untersuchung derjenigen homogenen Bereiche ausgingen, die der Theorie der Modul funktionen in mehreren Variablen zugrunde liegen. Die von ihnen zunachst im Hinblick auf diese Anwendungen entwickelten Methoden erwiesen sich dann auch flir Jordan-Algebren fiber beliebigen Korpern als adaquat. Bei der Gestaltung dieser Gedankengange wurden die Autoren von E. ARTIN in dessen letzten Lebensjahren tatkraftig unterstfitzt.
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