Lie Algebras and Lie Groups is popular PDF and ePub book, written by Jean-Pierre Serre in 2009-02-07, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Lie Algebras and Lie Groups can be Read Online from any device for your convenience.
Lie Algebras and Lie Groups Book PDF Summary
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).
Detail Book of Lie Algebras and Lie Groups PDF
- Author : Jean-Pierre Serre
- Release : 07 February 2009
- Publisher : Springer
- ISBN : 9783540706342
- Genre : Mathematics
- Total Page : 180 pages
- Language : English
- PDF File Size : 14,9 Mb
If you're still pondering over how to secure a PDF or EPUB version of the book Lie Algebras and Lie Groups by Jean-Pierre Serre, don't worry! All you have to do is click the 'Get Book' buttons below to kick off your Download or Read Online journey. Just a friendly reminder: we don't upload or host the files ourselves.
