Geometry of Lie Groups by B. RosenfeldGeometry of Lie Groups by B. Rosenfeld

Geometry of Lie Groups

byB. Rosenfeld, Bill Wiebe

Paperback | December 8, 2010

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This book represents the fruits of the author's many years of research and teaching. The introductory chapter contains the necessary background information from algebra, topology, and geometry of real spaces. Chapter 1 presents more specialized information on associative and nonassociative algebras and on Lie groups and algebras. In Chapters 2 through 6 geometric interpretations of all simple Lie groups of classes An, Bn, Cn, and Dn as well as of finite groups of Lie type are given. In Chapters 5 and 6 geometric interpretations of quasisimple and r-quasisimple Lie groups of the same classes are included. In Chapter 7, for the first time ever, geometric interpretations of all simple and quasisimple Lie groups of exceptional classes G2, F4, E6, E7, and E8 are given. The role of exercises is played by the assertions and theorems given without a full proof, but with the indication that they can be proved analogously to already proved theorems. Audience: The book will be of interest to graduate students and researchers in mathematics and physics.
Title:Geometry of Lie GroupsFormat:PaperbackDimensions:415 pages, 9.25 × 6.1 × 0.03 inPublished:December 8, 2010Publisher:Springer USLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:1441947698

ISBN - 13:9781441947697

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Table of Contents

Preface. 0. Structures of Geometry. I. Algebras and Lie Groups. II. Affine and Projective Geometries. III. Euclidean, Pseudo-Euclidean, Conformal and Pseudoconformal Geometries. IV. Elliptic, Hyperbolic, Pseudoelliptic, and Pseudohyperbolic Geometries. V. Quasielliptic, Quasihyperbolic, and Quasi-Euclidean Geometries. VI. Symplectic and Quasisymplectic Geometries. VII. Geometries of Exceptional Lie Groups. Metasymplectic Geometries. References. Index of Persons. Index of Subjects.