Enveloping Algebras: V14

by Diximier

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Title Statements

Full title :Enveloping Algebras : V14.

Edition Statements

Publication Date:2009.

Publication Statements

Publisher(s):Elsevier Science
Place of Publication:Burlington
Language:eng
Publication Date:2009.

The Physical Object

Description:1 online resource (393 pages)

Edition Identifiers

ISBN:9780444110770, 0444110771
oclc:ocn818814693
LC Classification:QA252.3
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. T…

Subjects

Algèbres de Lie Algèbres enveloppantes universelles Ideals (Algebra) Idéaux (Algèbre) Lie algebras Représentations des algèbres Representations Of Algebras Universal enveloping algebras