Translations of Mathematical Monographs 1997; 415 pp; hardcover Volume: 158 ISBN10: 0821845756 ISBN13: 9780821845752 List Price: US$135 Member Price: US$108 Order Code: MMONO/158
 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. Readership Graduate students, research mathematicians, mathematical physicists and theoretical physicists interested in global analysis and on manifolds. Table of Contents  Introduction
 Infinitedimensional calculus (Chapter I)
 Infinitedimensional manifolds (Chapter II)
 Infinitedimensional Lie groups (Chapter III)
 Geometric structures on orbits (Chapter IV)
 Fundamental theorems for differentiability (Chapter V)
 Groups of \(C^\infty\) diffeomorphisms on compact manifolds (Chapter VI)
 Linear operators (Chapter VII)
 Several subgroups of \({\scr D}(M)\) (Chapter VIII)
 Smooth extension theorems (Chapter IX)
 The group of diffeomorphisms on cotangent bundles (Chapter X)
 Pseudodifferential operators on manifolds (Chapter XI)
 Lie algebra of vector fields (Chapter XII)
 Quantizations (Chapter XIII)
 Poisson manifolds and quantum groups (Chapter XIV)
 Weyl manifolds (Chapter XV)
 Infinitedimensional Poisson manifolds (Chapter XVI)
 Appendix I
 Appendix II
 Appendix III
 References
 Index
