Elements of the Theory of Representations

A. A. Kirillov (Autor)

Buch | Softcover

XII, 318 Seiten

2011 | 1. Softcover reprint of the original 1st ed. 1976
Springer Berlin (Verlag)
978-3-642-66245-4 (ISBN)

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The translator of a mathematical work faces a task that is at once fascinating and frustrating. He has the opportunity of reading closely the work of a master mathematician. He has the duty of retaining as far as possible the flavor and spirit of the original, at the same time rendering it into a readable and idiomatic form of the language into which the translation is made. All of this is challenging. At the same time, the translator should never forget that he is not a creator, but only a mirror. His own viewpoints, his own preferences, should never lead him into altering the original, even with the best intentions. Only an occasional translator's note is permitted. The undersigned is grateful for the opportunity of translating Professor Kirillov's fine book on group representations, and hopes that it will bring to the English-reading mathematical public as much instruction and interest as it has brought to the translator. Deviations from the Russian text have been rigorously avoided, except for a number of corrections kindly supplied by Professor Kirillov. Misprints and an occasional solecism have been tacitly taken care of. The trans lation is in all essential respects faithful to the original Russian. The translator records his gratitude to Linda Sax, who typed the entire translation, to Laura Larsson, who prepared the bibliography (considerably modified from the original), and to Betty Underhill, who rendered essential assistance.

First Part. Preliminary Facts.-
1. Sets, Categories, Topology.-
2. Groups and Homogeneous Spaces.-
3. Rings and Module.-
4. Elements of Functional Analysis.-
5. Analysis on Manifolds.-
6. Lie Groups and Lie Algebras..- Second Part. Basic Concepts and Methods of the Theory of Representations.-
7. Representations of Groups.-
8. Decomposition of Representations.-
9. Invariant Integration.-
10. Group Algebras.-
11. Characters..-
12. Fourier Transforms and Duality.-
13. Induced Representations.-
14. Projective Representation.-
15. The Method of Orbits.- Third Part. Various Examples.-
16. Finite Groups.-
17. Compact Groups.-
18. Lie Groups and Lie Algebras.-
19. Examples of Wild Lie Groups.- A Short Historical Sketch and a Guide to the Literature.

Erscheint lt. Verlag	9.12.2011
Reihe/Serie	Grundlehren der mathematischen Wissenschaften
Übersetzer	E. Hewitt
Zusatzinfo	XII, 318 p.
Verlagsort	Berlin
Sprache	englisch
Maße	170 x 244 mm
Gewicht	580 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Schlagworte	Algebra • cohomology • Commutative Group • Darstellung • Darstellung (Math.) • Elements • finite group • Group representation • Lie algebra • Lie group • Locally compact group • manifold • Matrix • Operator algebra • representations • Ring • Transformation • transformation group
ISBN-10	3-642-66245-5 / 3642662455
ISBN-13	978-3-642-66245-4 / 9783642662454
Zustand	Neuware