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Softcover ISBN:  9781470426354 
Product Code:  MMONO/158.S 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445737 
Product Code:  MMONO/158.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Softcover ISBN:  9781470426354 
eBook ISBN:  9781470445737 
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 

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 infinitedimensional Lie groups involving the implicit function theorem and the Frobenius theorem. Omori treats as infinitedimensional 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.

Table of Contents

Chapters

Introduction

Chapter I. Infinitedimensional calculus

Chapter II. Infinitedimensional manifolds

Chapter III. Infinitedimensional 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. Infinitedimensional Poisson manifolds


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This book develops, from the viewpoint of abstract group theory, a general theory of infinitedimensional Lie groups involving the implicit function theorem and the Frobenius theorem. Omori treats as infinitedimensional 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. Infinitedimensional calculus

Chapter II. Infinitedimensional manifolds

Chapter III. Infinitedimensional 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. Infinitedimensional Poisson manifolds