Theory of Lie Groups (eBook)

Claude Chevalley (Autor)

eBook Download: EPUB

2018
224 Seiten
Dover Publications (Verlag)
978-0-486-82966-1 (ISBN)

Infos

The standard text on the subject for many years, this introductory treatment covers classical linear groups, topological groups, manifolds, analytic groups, differential calculus of Cartan, and compact Lie groups and their representations. 1946 edition.

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"e;Chevalley's most important contribution to mathematics is certainly his work on group theory. . . . [Theory of Lie Groups] was the first systematic exposition of the foundations of Lie group theory consistently adopting the global viewpoint, based on the notion of analytic manifold. This book remained the basic reference on Lie groups for at least two decades."e; — Bulletin of the American Mathematical Society Suitable for advanced undergraduate and graduate students of mathematics, this enduringly relevant text introduces the main basic principles that govern the theory of Lie groups. The treatment opens with an overview of the classical linear groups and of topological groups, focusing on the theory of covering spaces and groups, which is developed independently from the theory of paths. Succeeding chapters contain an examination of the theory of analytic manifolds as well as a combination of the notions of topological group and manifold that defines analytic and Lie groups. An exposition of the differential calculus of Cartan follows and concludes with an exploration of compact Lie groups and their representations.

Autor

Claude Chevalley (1909–84) received his doctorate in mathematics from the University of Paris in 1933 and was later at the Institute for Advanced Study in Princeton, New Jersey, and on the faculty of Columbia University. In the 1950s he returned to France and taught at his alma mater. In addition to his work on group theory, he made major contributions to several other areas of mathematics, including number theory and algebraic geometry. He was a member of the Bourbaki group and received the Cole Prize of the American Mathematical Society in 1941. His other books include Introduction to the Theory of Algebraic Functions of One Variable.

Inhalt

Table of Contents:IntroductionI. The Classical Linear GroupsII. Topological GroupsIII. ManifoldsIV. Analytic Groups. Lie GroupsV. The Differential Calculus of CartanVI. Compact Lie Groups and Their RepresentationsIndex.

Produkt-Details

• Erscheint lt. Verlag: 30.3.2018
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Schlagworte: abstract mathematics • algebraic equations • beginning algebra • covering application • experiments • learn math • math and science • math book • Math education • Mathematics • math instruction • math theory • Number Theory • Numerical analysis • phenomenon • Physics • physics and engineering • school • Science • scientists
• ISBN-10: 0-486-82966-9 / 0486829669
• ISBN-13: 978-0-486-82966-1 / 9780486829661