Enveloping Algebras: V14

by Diximier

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Title Statements

Full title :Enveloping Algebras : V14.

Edition Statements

Publication Date:2014.

Publication Statements

Publisher(s):Elsevier Science
Place of Publication:Saint Louis
Language:eng
Publication Date:2014.

Notes

4.2. Centre and core in the semi-simple case.

Enveloping Algebras.

The Physical Object

Description:1 online resource (393 pages).

Edition Identifiers

ISBN:9780444110770, 0444110771
oclc:on1058473565
LC Classification:QA252.3 ǂb D5713 1977eb
Dewey Decimal:512.2

Front Cover ; Enveloping Algebras; Copyright Page ; Contents ; Preface ; Preface to the English edition ; Notation ; Chapter 1. Lie algebras ; 1.1. General remarks ; 1.2. Representations ; 1.3. Solvable and nilpotent Lie algebras ; 1.4. The radical. The largest nilpotent ideal.

1.5. Semi-simple Lie algebras 1.6. Semi-simplicity of representations ; 1.7. Reductive Lie algebras ; 1.8. Representations of S(2, k); 1.9. Cartan subalgebras ; 1.10. The system of roots of a split semi-simple Lie algebra ; 1.11. Regular linear forms ; 1.12. Polarizations.

1.13. Symmetric semi-simple Lie algebras 1.14. Supplementary remarks ; Chapter 2. Enveloping algebras ; 2.1. The Poincaré-Birkhoff-Witt theorem; 2.2. The functor U ; 2.3. The filtration of the enveloping algebra ; 2.4. The canonical mapping of the symmetric algebra into the enveloping algebra.

2.5. The existence of finite-dimensional representations 2.6. The commutant of a simple module ; 2.7. The dual of the enveloping algebra ; 2.8. Supplementary remarks ; Chapter 3. Two-sided ideals in enveloping algebras ; 3.1. Primitive ideals and prime ideals.

3.2. The space of primitive ideals 3.3. The passage to an ideal of g ; 3.4. Extension …