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005 - DATE AND TIME OF LATEST TRANSACTION |
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20140310151441.0 |
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111105s2012 xxu| s |||| 0|eng d |
020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
International Standard Book Number |
9780387847948 |
|
978-0-387-84794-8 |
050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
Classification number |
QA252.3 |
|
Classification number |
QA387 |
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
Classification number |
512.55 |
Edition number |
23 |
|
Classification number |
512.482 |
Edition number |
23 |
264 #1 - |
-- |
New York, NY : |
-- |
Springer New York, |
-- |
2012. |
912 ## - |
-- |
ZDB-2-SMA |
100 1# - MAIN ENTRY--PERSONAL NAME |
Personal name |
Hilgert, Joachim. |
Relator term |
author. |
245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
Title |
Structure and Geometry of Lie Groups |
Medium |
[electronic resource] / |
Statement of responsibility, etc |
by Joachim Hilgert, Karl-Hermann Neeb. |
300 ## - PHYSICAL DESCRIPTION |
Extent |
X, 746 p. |
Other physical details |
online resource. |
440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE |
Title |
Springer Monographs in Mathematics, |
International Standard Serial Number |
1439-7382 |
505 0# - FORMATTED CONTENTS NOTE |
Formatted contents note |
Preface -- 1 Introduction -- Part I Matrix Groups -- 2 Concrete Matrix Groups -- 3 The Matrix Exponential Function -- 4 Linear Lie Groups -- Part II Lie Algebras.- 5 Elementary Structure Theory of Lie Algebras.- 6 Root Decomposition.- 7 Representation 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. |
520 ## - SUMMARY, ETC. |
Summary, etc |
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 on the authors' Lie-Gruppen und Lie-Algebren textbook from 1991, it presents the fundamental principles of Lie groups while 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 illustrate the correspondence between groups and their Lie algebras. In the second part of the book, the authors investigate the basic structure and representation theory of finite dimensional Lie algebras, such as the 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, the fourth part of the book deals with the structure theory of Lie groups, including some refined applications of the exponential function, various classes of Lie groups, and structural issues for general Lie groups. To round out the book's content, several appendices appear at the end of this last 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 and is 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. |
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
Topical term or geographic name as entry element |
Mathematics. |
|
Topical term or geographic name as entry element |
Algebra. |
|
Topical term or geographic name as entry element |
Topological Groups. |
|
Topical term or geographic name as entry element |
Global differential geometry. |
|
Topical term or geographic name as entry element |
Algebraic topology. |
|
Topical term or geographic name as entry element |
Mathematics. |
|
Topical term or geographic name as entry element |
Topological Groups, Lie Groups. |
|
Topical term or geographic name as entry element |
Differential Geometry. |
|
Topical term or geographic name as entry element |
Algebraic Topology. |
|
Topical term or geographic name as entry element |
Algebra. |
700 1# - ADDED ENTRY--PERSONAL NAME |
Personal name |
Neeb, Karl-Hermann. |
Relator term |
author. |
710 2# - ADDED ENTRY--CORPORATE NAME |
Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
773 0# - HOST ITEM ENTRY |
Title |
Springer eBooks |
776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
Display text |
Printed edition: |
International Standard Book Number |
9780387847931 |
856 40 - ELECTRONIC LOCATION AND ACCESS |
Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-0-387-84794-8 |
942 ## - ADDED ENTRY ELEMENTS (KOHA) |
Source of classification or shelving scheme |
|
Item type |
E-Book |