Theory of Continuous Groups (Paperback)

Charles Loewner

ISBN 10: 0486462927 / ISBN 13: 9780486462929

Editore: Dover Publications Inc., New York, 2008

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Paperback. Professor of Mathematics at Stanford University from 1950 until his death in 1968, Charles Loewner occasionally taught as a Visiting Professor at the University of California at Berkeley. After his 1955 course at Berkeley on continuous groups, Loewner's lectures were reproduced in the form of mimeographed notes. The professor had intended to develop these notes into a book, but the project was still in formative stages at the time of his death. The 1971 edition compiles edited and updated versions of Professor Loewner's original fourteen lectures, making them available in permanent form.Professor Loewner's interest in continuous groups-particularly with respect to applications in geometry and analysis-began with his study of Sophus Lie's three-volume work on transformation groups. He was able 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-primarily geometric in character-reflect the professor's unique view and treatment of continuous groups. These 14 lectures by a renowned educator focus on applications of continuous groups in geometry and analysis. Their unique perspectives are illustrated by numerous inventive geometric examples. 1971 edition. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Codice articolo 9780486462929

Dati bibliografici

• Titolo: Theory of Continuous Groups (Paperback)
• Editore: Dover Publications Inc., New York
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 0486462927
• ISBN 13: 9780486462929
• Rilegatura: Paperback
• Condizione: new

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Riassunto

Professor of Mathematics at Stanford University from 1950 until his death in 1968, Charles Loewner occasionally taught as a Visiting Professor at the University of California at Berkeley. After his 1955 course at Berkeley on continuous groups, Loewner's lectures were reproduced in the form of mimeographed notes. The professor had intended to develop these notes into a book, but the project was still in formative stages at the time of his death. The 1971 edition compiles edited and updated versions of Professor Loewner's original fourteen lectures, making them available in permanent form.
Professor Loewner's interest in continuous groups—particularly with respect to applications in geometry and analysis—began with his study of Sophus Lie's three-volume work on transformation groups. He was able 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—primarily geometric in character—reflect the professor's unique view and treatment of continuous groups.

Contenuti

Preface Lecture I: Transformation Groups; Similarity Lecture II: Representations of Groups; Combinations of Representations; Similarity and Reducibility Lecture III: Representations of Cyclic Groups; Representations of Finite Abelian Groups; Representations of Finite Groups Lecture IV: Representations of Finite Groups (cont.); Characters Lecture V: Representations of Finite Groups (conc.); Introduction to Differentiable Manifolds; Tensor Calculus on a Manifold Lecture VI: Quantities, Vectors, and Tensors; Generation of Quantities by Differentiation; Commutator of Two Contravariant Vector Fields; Hurwitz Integration on a Group Manifold Lecture VII: Hurwitz Integration on a Group Manifold (cont.); Representation of Compact Groups; Existence of Representations Lecture VIII: Representation of Compact Groups (cont.); Characters; Examples Lecture IX: Lie Groups; Infinitesimal Transformations on a Manifold Lecture X: Infinitesimal Transformations of a Group; Examples; Geometry on the Group Space Lecture XI: Parallelism; First Fundamental Theorem of Lie Groups; Mayer-Lie Systems Lecture XII: The Sufficiency Proof; First Fundamental Theorem; Converse; Second Fundamental Theorem; Converse Lecture XIII: Converse of the Second Fundamental Theorem (cont.); Concept of Group Germ Lecture XIV: Converse of the Third Fundamental Theorem; The Helmholtz-Lie Problem Index