Lie Algebras (Dover Books on Mathematics) - Softcover

Jacobson, Nathan

Softcover

ISBN 10: 0486638324 ISBN 13: 9780486638324

Verlag: Dover Publications, 1979

Inhaltsangabe

Lie group theory, developed by M. Sophus Lie in the nineteenth century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a text for graduate courses.
Chapter 1 introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Cartan&;s criterion and its consequences, and split semi-simple Lie algebras. Chapter 5, on universal enveloping algebras, provides the abstract concepts underlying representation theory. The basic results on representation theory are given in three succeeding chapters: the theorem of Ado-Iwasawa, classification of irreducible modules, and characters of the irreducible modules. In Chapter 9 the automorphisms of semi-simple Lie algebras over an algebraically closed field of characteristic zero are determined. These results are applied in Chapter 10 to the problems of sorting out the simple Lie algebras over an arbitrary field. The reader, to fully benefit from this tenth chapter, should have some knowledge about the notions of Galois theory and some of the results of the Wedderburn structure theory of associative algebras.
Nathan Jacobson, presently Henry Ford II Professor of Mathematics at Yale University, is a well-known authority in the field of abstract algebra. His book, Lie Algebras, is a classic handbook both for researchers and students. Though it presupposes knowledge of linear algebra, it is not overly theoretical and can be readily used for self-study.

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Über die Autorin bzw. den Autor

One of the world's leading researchers in abstract algebra, Nathan Jacobson (1910-95) taught at several prominent universities, including the University of Chicago, Johns Hopkins, and Yale.

Details zur Ausgabe

• Verlag: Dover Publications
• Erscheinungsdatum: 1979
• Sprache: Englisch
• ISBN 10: 0486638324
• ISBN 13: 9780486638324
• Einband: Taschenbuch
• Anzahl der Seiten: 331
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Soc. Agr. La Raia Ss; http://www.la-raia.it; ; Strada Monterotondo, 79; Novi Ligure; 15067; Italien