Lie Algebras and Lie Groups by Jean-Pierre Serre
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 (R)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).
Professor Jean-Pierre Serre ist ein renommierter franzosischer Mathematiker am College de France, Paris.
| SKU | Unavailable |
| ISBN 13 | 9783540550082 |
| ISBN 10 | 3540550089 |
| Title | Lie Algebras and Lie Groups |
| Author | Jean Pierre Serre |
| Series | Lecture Notes In Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer-Verlag Berlin and Heidelberg GmbH & Co. KG |
| Year published | 1992-03-11 |
| Number of pages | 173 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |