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eBook ISBN: | 978-1-4704-4573-7 |
Product Code: | MMONO/158.E |
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Softcover ISBN: | 978-1-4704-2635-4 |
eBook: ISBN: | 978-1-4704-4573-7 |
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MAA Member Price: | $288.00 $218.25 |
AMS Member Price: | $256.00 $194.00 |
Softcover ISBN: | 978-1-4704-2635-4 |
Product Code: | MMONO/158.S |
List Price: | $165.00 |
MAA Member Price: | $148.50 |
AMS Member Price: | $132.00 |
eBook ISBN: | 978-1-4704-4573-7 |
Product Code: | MMONO/158.E |
List Price: | $155.00 |
MAA Member Price: | $139.50 |
AMS Member Price: | $124.00 |
Softcover ISBN: | 978-1-4704-2635-4 |
eBook ISBN: | 978-1-4704-4573-7 |
Product Code: | MMONO/158.S.B |
List Price: | $320.00 $242.50 |
MAA Member Price: | $288.00 $218.25 |
AMS Member Price: | $256.00 $194.00 |
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Book DetailsTranslations of Mathematical MonographsVolume: 158; 1997; 415 ppMSC: Primary 58; Secondary 22; 81
This book develops, from the viewpoint of abstract group theory, a general theory of infinite-dimensional Lie groups involving the implicit function theorem and the Frobenius theorem. Omori treats as infinite-dimensional Lie groups all the real, primitive, infinite transformation groups studied by E. Cartan. The book discusses several noncommutative algebras such as Weyl algebras and algebras of quantum groups and their automorphism groups. The notion of a noncommutative manifold is described, and the deformation quantization of certain algebras is discussed from the viewpoint of Lie algebras.
This edition is a revised version of the book of the same title published in Japanese in 1979.
ReadershipGraduate students, research mathematicians, mathematical physicists and theoretical physicists interested in global analysis and on manifolds.
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Table of Contents
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Chapters
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Introduction
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Chapter I. Infinite-dimensional calculus
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Chapter II. Infinite-dimensional manifolds
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Chapter III. Infinite-dimensional Lie groups
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Chapter IV. Geometric structures on orbits
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Chapter V. Fundamental theorems for differentiability
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Chapter VI. Groups of $C^\infty $ diffeomorphisms on compact manifolds
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Chapter VII. Linear operators
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Chapter VIII. Several subgroups of $\mathcal {D}(M)$
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Chapter IX. Smooth extension theorems
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Chapter X. Group of diffeomorphisms on cotangent bundles
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Chapter XI. Pseudodifferential operators on manifolds
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Chapter XII. Lie algebra of vector fields
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Chapter XIII. Quantizations
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Chapter XIV. Poisson manifolds and quantum groups
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Chapter XV. Weyl manifolds
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Chapter XVI. Infinite-dimensional Poisson manifolds
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This book develops, from the viewpoint of abstract group theory, a general theory of infinite-dimensional Lie groups involving the implicit function theorem and the Frobenius theorem. Omori treats as infinite-dimensional Lie groups all the real, primitive, infinite transformation groups studied by E. Cartan. The book discusses several noncommutative algebras such as Weyl algebras and algebras of quantum groups and their automorphism groups. The notion of a noncommutative manifold is described, and the deformation quantization of certain algebras is discussed from the viewpoint of Lie algebras.
This edition is a revised version of the book of the same title published in Japanese in 1979.
Graduate students, research mathematicians, mathematical physicists and theoretical physicists interested in global analysis and on manifolds.
-
Chapters
-
Introduction
-
Chapter I. Infinite-dimensional calculus
-
Chapter II. Infinite-dimensional manifolds
-
Chapter III. Infinite-dimensional Lie groups
-
Chapter IV. Geometric structures on orbits
-
Chapter V. Fundamental theorems for differentiability
-
Chapter VI. Groups of $C^\infty $ diffeomorphisms on compact manifolds
-
Chapter VII. Linear operators
-
Chapter VIII. Several subgroups of $\mathcal {D}(M)$
-
Chapter IX. Smooth extension theorems
-
Chapter X. Group of diffeomorphisms on cotangent bundles
-
Chapter XI. Pseudodifferential operators on manifolds
-
Chapter XII. Lie algebra of vector fields
-
Chapter XIII. Quantizations
-
Chapter XIV. Poisson manifolds and quantum groups
-
Chapter XV. Weyl manifolds
-
Chapter XVI. Infinite-dimensional Poisson manifolds