Overview
- Authors:
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D. H. Sattinger
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School of Mathematics, University of Minnesota, Minneapolis, USA
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O. L. Weaver
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Department of Physics, Kansas State University, Manhattan, USA
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Table of contents (14 chapters)
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Lie Groups and Algebras
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- D. H. Sattinger, O. L. Weaver
Pages 3-20
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- D. H. Sattinger, O. L. Weaver
Pages 21-31
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- D. H. Sattinger, O. L. Weaver
Pages 32-40
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- D. H. Sattinger, O. L. Weaver
Pages 41-54
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Differential Geometry and Lie Groups
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- D. H. Sattinger, O. L. Weaver
Pages 57-75
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- D. H. Sattinger, O. L. Weaver
Pages 76-88
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- D. H. Sattinger, O. L. Weaver
Pages 89-108
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- D. H. Sattinger, O. L. Weaver
Pages 109-115
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Algebraic Theory
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Front Matter
Pages 117-117
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- D. H. Sattinger, O. L. Weaver
Pages 119-129
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- D. H. Sattinger, O. L. Weaver
Pages 130-152
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- D. H. Sattinger, O. L. Weaver
Pages 153-159
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Representation Theory
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Front Matter
Pages 161-161
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- D. H. Sattinger, O. L. Weaver
Pages 163-180
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- D. H. Sattinger, O. L. Weaver
Pages 181-186
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Applications
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Front Matter
Pages 187-187
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- D. H. Sattinger, O. L. Weaver
Pages 189-207
About this book
This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselvesto the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.
Authors and Affiliations
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School of Mathematics, University of Minnesota, Minneapolis, USA
D. H. Sattinger
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Department of Physics, Kansas State University, Manhattan, USA
O. L. Weaver