MARC details
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04329nam a22005055i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
978-1-4612-6398-2 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20210921163821.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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121227s1972 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781461263982 |
| -- |
978-1-4612-6398-2 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-1-4612-6398-2 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA150-272 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBF |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT002000 |
| Source |
bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBF |
| Source |
thema |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Humphreys, J.E. |
| Relator term |
author. |
| Relator code |
aut |
| -- |
http://id.loc.gov/vocabulary/relators/aut |
| 245 10 - TITLE STATEMENT |
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| Title |
Introduction to Lie Algebras and Representation Theory |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc |
by J.E. Humphreys. |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
1st ed. 1972. |
| 264 #1 - |
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| -- |
New York, NY : |
| -- |
Springer New York : |
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Imprint: Springer, |
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1972. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
XIII, 173 p. |
| Other physical details |
online resource. |
| 336 ## - |
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text |
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txt |
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rdacontent |
| 337 ## - |
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computer |
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c |
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rdamedia |
| 338 ## - |
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online resource |
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cr |
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rdacarrier |
| 347 ## - |
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text file |
| -- |
PDF |
| -- |
rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Graduate Texts in Mathematics, |
| International Standard Serial Number |
0072-5285 ; |
| Volume number/sequential designation |
9 |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
I. Basic Concepts -- 1. Definitions and first examples -- 2. Ideals and homomorphisms -- 3. Solvable and nilpotent Lie algebras -- II. Semisimple Lie Algebras -- 4. Theorems of Lie and Cartan -- 5. Killing form -- 6. Complete reducibility of representations -- 7. Representations of sl (2, F) -- 8. Root space decomposition -- III. Root Systems -- 9. Axiomatics -- 10. Simple roots and Weyl group -- 11. Classification -- 12. Construction of root systems and automorphisms -- 13. Abstract theory of weights -- IV. Isomorphism and Conjugacy Theorems -- 14. Isomorphism theorem -- 15. Cartan subalgebras -- 16. Conjugacy theorems -- V. Existence Theorem -- 17. Universal enveloping algebras -- 18. The simple algebras -- VI. Representation Theory -- 20. Weights and maximal vectors -- 21. Finite dimensional modules -- 22. Multiplicity formula -- 23. Characters -- 24. Formulas of Weyl, Kostant, and Steinberg -- VII. Chevalley Algebras and Groups -- 25. Chevalley basis of L -- 26. Kostant's Theorem -- 27. Admissible lattices -- References -- Afterword (1994) -- Index of Terminology -- Index of Symbols. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebra. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebra. |
| -- |
https://scigraph.springernature.com/ontologies/product-market-codes/M11000 |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Display text |
Printed edition: |
| International Standard Book Number |
9780387900520 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Display text |
Printed edition: |
| International Standard Book Number |
9781489984005 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Printed edition: |
| International Standard Book Number |
9780387900537 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Display text |
Printed edition: |
| International Standard Book Number |
9781461263999 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
Graduate Texts in Mathematics, |
| -- |
0072-5285 ; |
| Volume number/sequential designation |
9 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://doi.org/10.1007/978-1-4612-6398-2">https://doi.org/10.1007/978-1-4612-6398-2</a> |
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ZDB-2-BAE |
