Vorlesungen Über Geometrie Der Algebren: Geometrien Von Möbius, Laguerre-Lie, Minkowski in Einheitlicher Und Grundlagengeometrischer Behandlung

Name: Vorlesungen Über Geometrie Der Algebren: Geometrien Von Möbius, Laguerre-Lie, Minkowski in Einheitlicher Und Grundlagengeometrischer Behandlung
Brand: Springer
SKU: 9783642886713
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by Walter Benz

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ISBN13: 9783642886713
Binding: Paperback
Subject: N/A
Publisher: Springer
Publisher Imprint: Springer
Publication Date: May 19, 2012
Pages: 368
Original Price: EUR 65.41
Language: German
Edition: Softcover Repri
Item Weight: 508 grams
BISAC Subject(s): General

About The Book

Mit Hilfe der reellen Algebren der komplexen Zahlen, dualen Zahlen, anormal-komplexen Zahlen konnen Mobiusgeometrie (Geometrie der Kreise), Laguerre- bzw. Liegeometrie, pseudoeuklidische Geometrie (Minkowskigeometrie) behandelt werden. Das geschieht fiir die erst- genannte Geometrie in der Geometrie der komplexen Zahlen. - Diese Zusammenhange bilden den Hintergrund des vorliegenden Buches. In Verfolg axiomatischer Begrtindungen der augegebenen Geometrien wurde del" Bereich der vorweg genannten reellen Algebren ausgedehnt: 1st Sl' ein quadratisch nicht abgeschlossener kommutativer Korper, 2 eine quadratische Korpererweiterung von Sl', so gehort zur Algebra 2 tiber Sl' eine miquelsche Mobiusebene und jede miquelsche Mobiusebene kann mit Hilfe einer solchen Algebra beschrieben werden. Entsprechendes gilt fUr Laguerre-und Minkowskigeometrie. Es gibt genau 5 paarweise nicht isomorphe kommutative, assoziative Algebren mit Eins yom Rang 3 tiber den reellen Zahlen; diese beschreiben Geometrien raumlicher Kurvensysteme. Beliebige kommutative Korpererweiterungen eines kommutativen Korpers ftihren zu miquelschen Geometrien, die eng ver- wandt sind mit den miquelschen Mobiusebenen, insofem als nur ein impliziter Beriihrbegriff an die Stelle des bei Mobiusebenen expliziten zu treten hat. Weitere Algebrengeometrien beanspruchen im hier verfolgten Rahmen Interesse, wie etwa die Quatemionen tiber den komplexen Zah- len, die die Geometrie der Kreise und Kugeln im vierdimensionalen Raum beschreiben. Das vorliegende Buch ist aus Vorlesungen hervorgegangen, die der Autor an mehreren in-und auslandischen Universitaten gehalten hat. An den Anfang der Untersuchungen habe ich die klassischen Fane, nam- lich die Geometrien von Mobius, Laguerre-Lie, Minkowski gestellt. Ich mochte hiermit Tatsachenmaterial bereitstellen, das spat ere Ansatze motiviert.

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