TY  - BOOK
AU  - 
AU  - 
ED  - SpringerLink (Online service)
TI  - Structure and Geometry of Lie Groups
T2  - Springer Monographs in Mathematics,
SN  - 9780387847948
AV  - QA252.3 
U1  - 512.55 23
PY  - 2012///
CY  - New York, NY
PB  - Springer New York
KW  - Mathematics
KW  - Algebra
KW  - Topological Groups
KW  - Global differential geometry
KW  - Algebraic topology
KW  - Topological Groups, Lie Groups
KW  - Differential Geometry
KW  - Algebraic Topology
N1  - Preface -- 1 Introduction -- Part I Matrix Groups -- 2 Concrete Matrix Groups -- 3The Matrix Exponential Function -- 4Linear Lie Groups -- Part II Lie Algebras.-5Elementary Structure Theory of Lie Algebras.-6Root Decomposition.-7Representation Theory of Lie Algebras -- Part III Manifolds and Lie Groups.-8 Smooth Manifolds -- 9 Basic Lie Theory -- 10 Smooth Actions of Lie Groups -- Part IV Structure Theory of Lie Groups -- 11 Normal Subgroups, Nilpotemt and Solvable Lie Groups -- 12 Compact Lie Groups -- 13 Semisimple Lie Groups -- 14 General Structure Theory -- 15 Complex Lie Groups -- 16 Linearity of Lie Groups -- 17 Classical Lie Groups -- 18 Nonconnected Lie Groups -- Part V Appendices -- A Basic Covering Theory -- B Some Multilinear Algebra -- C Some Functional Analysis -- D Hints to Exercises -- References -- Index; ZDB-2-SMA
N2  - This text is designed as an introduction to Lie groups and their actions on manifolds, one that is accessible both to a broad range of mathematicians and to graduate students.Building onthe authors' Lie-Gruppen und Lie-Algebren textbook from 1991, itpresents the fundamental principles of Lie groupswhile incorporating the past 20 years of the authors' teaching and research, and giving due emphasis to the role played by differential geometry in the field. The text is entirely self contained,and provides ample guidance to students with the presence of many exercises and selected hints. The work begins with a study of matrix groups, which serve as examples to concretely and directly illustratethe correspondence between groups and their Lie algebras. In the second part of the book, theauthorsinvestigate the basic structure and representation theory of finite dimensional Lie algebras,such asthe rough structure theory relevant to the theorems of Levi and Malcev, the fine structure of semisimple Lie algebras (root decompositions), and questions related to representation theory. In the third part of the book, the authors turn to global issues, most notably the interplay between differential geometry and Lie theory. Finally, thefourth part of the book deals with the structure theory of Lie groups, includingsome refined applications of the exponential function, various classes of Lie groups, andstructural issues for general Lie groups. To round out the book's content, several appendices appear at the end of thislast part. Containing a wealth of useful information, including new results, Structure and Geometry of Lie Groups provides a unique perspective on the study of Lie groups andis a valuable addition to the literature. Prerequisites are generally kept to a minimum, and various pedagogical features make it an excellent supplemental text for graduate students. However, the work also contains much that will be of interest to more advanced audiences, and can serve as a useful research reference in the field
UR  - http://dx.doi.org/10.1007/978-0-387-84794-8
ER  -