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Theory of continuous groups

Loewner, Charles, 1893-1968

Verlag: Notes by Harley Flanders and Murray H. Protter. Cambridge, Mass., MIT Press, 1971, 1971
ISBN 10: 0262060418 / ISBN 13: 9780262060417
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Titel: Theory of continuous groups

Verlag: Notes by Harley Flanders and Murray H. Protter. Cambridge, Mass., MIT Press, 1971

Erscheinungsdatum: 1971

Einband: Hardcover

Zustand des Schutzumschlags: Dust Jacket Included


, ix, 110pp., dust-jacket chipped and torn along top edge, very good orange-brown cloth, Mathematicians of our time, volume 1. Karl (or Karel) Löwner - the original spelling - was born near Prague and got his Ph.D. in mathematics from Prague University; he taught in Berlin from 1922-1928 and received a post in Prague, then escaped to the US in 1939. Supported by John von Neumann and Eugene Wigner, who cited his 1933 essay on matrix functions, he held a number of minor positions before landing at Stanford (1951-1968). ISBN 0262060418 . Buchnummer des Verkäufers 70996

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Inhaltsangabe: Charles Loewner, Professor of Mathematics at Stanford University from 1950 until his death in 1968, was a Visiting Professor at the University of California at Berkeley on five separate occasions. During his 1955 visit to Berkeley he gave a course on continuous groups, and his lectures were reproduced in the form of mimeographed notes. Loewner planned to write a detailed book on continuous groups based on these lecture notes, but the project was still in the formative stage at the time of his death. Since the notes themselves have been out of print for several years, Professor Harley Flanders, Department of Mathematics, Tel Aviv University, and Professor Murray Protter, Department of Mathematics, University of California, Berkeley, have taken this opportunity to revise and correct the original fourteen lectures and make them available in permanent form.Loewner became interested in continuous groups--particularly with respect to possible applications in geometry and analysis--when he studied the three volume work on transformation groups by Sophus Lie. He managed to reconstruct a coherent development of the subject by synthesizing Lie's numerous illustrative examples, many of which appeared only as footnotes. The examples contained in this book are primarily geometric in character and reflect the unique way in which Loewner viewed each of the topics he treated.This book is part of the series "Mathematicians of Our Time, " edited by Professor Gian-Carlo Rota, Department of Mathematics, Massachusetts Institute of Technology."Contents: " Transformation Groups; Similarity; Representations of Groups; Combinations of Representations; Similarity and Reducibility; Representations of Cyclic Groups; Representations of Finite Abelian Groups; Representations of Finite Groups; Characters; Introduction to Differentiable Manifolds; Tensor Calculus on a Manifold; Quantities, Vectors, Tensors; Generation of Quantities by Differentiation; Commutator of Two Covariant Vector Fields; Hurwitz Integration on a Group Manifold; Representation of Compact Groups; Existence of Representations; Characters; Examples; Lie Groups; Infinitesimal Transformation on a Manifold; Infinitesimal Transformations on a Group; Examples; Geometry on the Group Space; Parallelism; First Fundamental Theorem of Lie Groups; Mayer-Lie Systems; The Sufficiency Proof; First Fundamental Theorem, Converse; Second Fundamental Theorem, Converse; Concept of Group Germ; Converse of the Third Fundamental Theorem; The Helmholtz-Lie Problem.

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