

Av Jean-Pierre Serre, 1992.Del av serien Lecture Notes in Mathematics.
1964 Lectures given at Harvard University
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).
Ikke tilgjengelig for Klikk&Hent
Midlertidig tomt på lager
Bestillingsvare. Forventes sendt om ca 11 dager

Av Jean-Pierre Serre, 1992.Del av serien Lecture Notes in Mathematics.
1964 Lectures given at Harvard University
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).
Ikke tilgjengelig for Klikk&Hent
Midlertidig tomt på lager
Bestillingsvare. Forventes sendt om ca 11 dager
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