{"product_id":"9783540550082-lie-algebras-lie-groups-5e","title":"Lie Algebras and Lie Groups","description":"\u003cmeta content=\"text\/html; charset=utf-8\" http-equiv=\"Content-Type\"\u003e\u003cp\u003e\u003cspan\u003e1964 Lectures given at Harvard University\u003cbr\u003eReproduces J-P Serre's 1964 Harvard lectures. This book aims to introduce the reader to the \"Lie dictionary: Lie algebras and Lie groups\". It provides emphasis on formal groups (in the Lie group part) and the use of analytic manifolds on p-adic fields. Intended for graduate students, it assumes some knowledge of algebra and calculus.\u003cbr\u003eThe 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).\u003cbr\u003e\u003cbr\u003e\u003c\/span\u003e\u003c\/p\u003e","brand":"Rarewaves","offers":[{"title":"Default Title","offer_id":54811025703286,"sku":"9783540550082","price":37.21,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0092\/7504\/8033\/files\/stand_31456917.jpg?v=1732727518","url":"https:\/\/www.rarewaves.com\/products\/9783540550082-lie-algebras-lie-groups-5e","provider":"Rarewaves.com","version":"1.0","type":"link"}