Lie Algebras and Lie Groups
1964 Lectures given at Harvard University
(Sprache: Englisch)
The main general theorems on Lie Algebras are covered, roughly the content of Bourbaki's Chapter I. I have added some results on free Lie algebras, which are useful, both for Lie's theory itself (Campbell-Hausdorff formula) and for applications to...
Leider schon ausverkauft
versandkostenfrei
Buch
37.40 €
Produktdetails
Produktinformationen zu „Lie Algebras and Lie Groups “
Klappentext zu „Lie Algebras and Lie Groups “
The main general theorems on Lie Algebras are covered, roughly the content of Bourbaki's Chapter I. I have added some results on free Lie algebras, which are useful, both for Lie's theory itself (Campbell-Hausdorff formula) and for applications to pro-Jrgroups. of time prevented me from including the more precise theory of Lack semisimple Lie algebras (roots, weights, etc.); but, at least, I have given, as a last Chapter, the typical case ofal,.. This part has been written with the help of F.Raggi and J.Tate. I want to thank them, and also Sue Golan, who did the typing for both parts. Jean-Pierre Serre Harvard, Fall 1964 Chapter I. Lie Algebras: Definition and Examples Let Ie be a commutativering with unit element, and let A be a k-module, then A is said to be a Ie-algebra if there is given a k-bilinear map A x A~ A (i.e., a k-homomorphism A0" A -+ A). As usual we may define left, right and two-sided ideals and therefore quo tients. Definition 1. A Lie algebra over Ie isan algebrawith the following properties: 1). The map A0i A -+ A admits a factorization A ®i A -+ A2A -+ A i.e., ifwe denote the imageof(x,y) under this map by [x,y) then the condition becomes for all x e k. [x,x)=0 2). (lx,II], z]+ny, z), x) + ([z,xl, til = 0 (Jacobi's identity) The condition 1) implies [x,1/]=-[1/,x).
Inhaltsverzeichnis zu „Lie Algebras and Lie Groups “
- Part I: Lie Algebras: Lie Algebras:... Definition and Examples
... Filtered Groups and Lie Algebras
... Filtered Groups and Lie Algebras
... Universal Algebra of a Lie Algebra
... Free Lie Algebras
... Nilpotent and Solvable Lie Algebras
... Semisimple Lie Algebras
... Representations of sln
- Part II: Complete Fields:
... Analytic Functions
... Analytic Manifolds
... Analytic Groups
... Lie Theory.
Autoren-Porträt von Jean-Pierre Serre
Professor Jean-Pierre Serre ist ein renommierter französischer Mathematiker am College de France in Paris.
Bibliographische Angaben
- Autor: Jean-Pierre Serre
- 2005, 2nd ed. Corr. pr., 173 Seiten, Maße: 15,6 x 23,8 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 3540550089
- ISBN-13: 9783540550082
- Erscheinungsdatum: 20.10.2005
Sprache:
Englisch
Kommentar zu "Lie Algebras and Lie Groups"
0 Gebrauchte Artikel zu „Lie Algebras and Lie Groups“
Zustand | Preis | Porto | Zahlung | Verkäufer | Rating |
---|
Schreiben Sie einen Kommentar zu "Lie Algebras and Lie Groups".
Kommentar verfassen