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Darstellungstheorie Von Endlichen Gruppen by Wolfgang Müller

Darstellungstheorie Von Endlichen Gruppen

by Wolfgang Müller
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Book cover type: Paperback
  • ISBN13: 9783519020608
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Publication Date:
  • Pages: 215
  • Original Price: EUR 42.05
  • Language: German
  • Edition: 1980
  • Item Weight: 268 grams
  • BISAC Subject(s): Engineering (General)

Dieses Skriptum ist aus Vorlesungen hervorgegangen, die ich an den Universitaten MUnchen und Bayreuth gehalten habe, und gibt eine EinfUhrung in die Darstellungstheorie endlicher Gruppen, die etwa dem Umfang einer zweisemestrigen Vorlesung entspricht. Das Skriptum ist insbesondere fUr Studenten der Mathematik nach den VorprUfungen gedacht, wenn auch an algebraischem Grundwissen nur elementare Kenntnisse der Kerper-, Gruppen- und Modultheorie vorausgesetzt werden. Der Inhalt besteht aus zwei Teilen. Der erste Teil befaBt sich mit der gewehnlichen Darstellungstheorie, bei der man Gruppen in halbeinfache Algebren Uber einem Kerper einbettet und die Dar- stellungen der Gruppen aus den Moduln Uber diesen Algebren er- halt. Der zweite Teil behandelt die modulare Darstellungstheorie. Dabei werden zunachst die Grundlagen aus der Ring- und Modultheorie dargelegt. Dann wird auf die Theorie der nicht-halbeinfachen Gruppenalgebren eingegangen, wie sie vor allem von D.G. Higman, J.A. Green und G.O. Michler aufgebaut worden ist. SchlieBlich wird die klassische Methode der modularen Darstellungstheorie entwickelt, bei der man von einem bewerteten Kerper mit der Charakteristik 0 zu dem Radikalfaktorring des zugeherigen Bewer- tungsrings Ubergeht. Einen genaueren Uberblick gewinnt der Leser durch das Inhalts- verzeichnis sowie den schematischen Leitfaden, der die logische Abhangigkeit der einzelnen Abschnitte anzeigt. Insbesondere ist zum Verstandnis des zweiten Teils, wenn man von den Abschnitten 10.4 und 10.5 absieht, vom ersten Teil nur die Kenntnis der Abschnitte 1.1 bis 1.3 und die Definition 2.11 der Gruppen- algebra notwendig.

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