{"product_id":"lie-groups-and-lie-algebras-chapters-7-9-elements-of-mathematics","title":"Lie Groups and Lie Algebras: Chapters 7-9 (Elements of Mathematics)","description":"\u003ch3\u003e\u003cstrong\u003eBook Details\u003c\/strong\u003e\u003c\/h3\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cstrong\u003ePublisher\u003c\/strong\u003e: Springer\u003c\/p\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor\u003c\/strong\u003e: N. Bourbaki\u003c\/p\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cstrong\u003eLanguage\u003c\/strong\u003e: English\u003c\/p\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cstrong\u003eEdition\u003c\/strong\u003e: First Edition\u003c\/p\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cstrong\u003eISBN\u003c\/strong\u003e: 9783540688518\u003c\/p\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cstrong\u003ePages\u003c\/strong\u003e: 445\u003c\/p\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cstrong\u003eCover\u003c\/strong\u003e: Paperback\u003c\/p\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003cstrong\u003eDimensions\u003c\/strong\u003e: 9.2 x 6.1 x 1.0 inches\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch3\u003e\u003cstrong\u003eAbout The Book\u003c\/strong\u003e\u003c\/h3\u003e\n\u003cp\u003e\u003cem\u003eLie Groups and Lie Algebras: Chapters 7–9\u003c\/em\u003e by \u003cstrong\u003eN. Bourbaki\u003c\/strong\u003e is the final volume in the legendary mathematical series covering the theory of \u003cstrong\u003eLie groups and Lie algebras\u003c\/strong\u003e. This softcover reprint in English provides a rigorous and detailed exposition of advanced topics including the \u003cstrong\u003estructure and representation theory\u003c\/strong\u003e of \u003cstrong\u003esemi-simple Lie algebras\u003c\/strong\u003e and \u003cstrong\u003ecompact Lie groups\u003c\/strong\u003e, completing the material introduced in Chapters 1 to 6.\u003c\/p\u003e\n\u003cp\u003eChapter 7 explores \u003cstrong\u003eCartan subalgebras\u003c\/strong\u003e, \u003cstrong\u003eregular elements\u003c\/strong\u003e, and \u003cstrong\u003econjugacy theorems\u003c\/strong\u003e, forming the backbone of the structure theory of Lie algebras. Chapter 8 shifts focus to \u003cstrong\u003esplit semi-simple Lie algebras\u003c\/strong\u003e, detailing their \u003cstrong\u003eroot systems\u003c\/strong\u003e, and develops a comprehensive treatment of \u003cstrong\u003efinite-dimensional modules\u003c\/strong\u003e, culminating in \u003cstrong\u003eWeyl's character formula\u003c\/strong\u003e and the \u003cstrong\u003etheory of Chevalley orders\u003c\/strong\u003e.\u003c\/p\u003e\n\u003cp\u003eChapter 9 is a masterful treatment of \u003cstrong\u003ecompact Lie groups\u003c\/strong\u003e, beginning with \u003cstrong\u003emaximal tori\u003c\/strong\u003e, \u003cstrong\u003eWeyl groups\u003c\/strong\u003e, and their \u003cstrong\u003eroot systems\u003c\/strong\u003e, and progressing to an in-depth study of \u003cstrong\u003erepresentation theory\u003c\/strong\u003e. It skillfully integrates \u003cstrong\u003eharmonic analysis\u003c\/strong\u003e through applications of integration, establishing Weyl’s formula in the context of compact groups. The chapter concludes with a study of \u003cstrong\u003egroup actions on manifolds\u003c\/strong\u003e, extending the utility of Lie theory into geometric and topological realms.\u003c\/p\u003e\n\u003cp\u003eRenowned for its mathematical precision and depth, this volume is an indispensable reference for researchers, graduate students, and professionals in \u003cstrong\u003epure mathematics\u003c\/strong\u003e, \u003cstrong\u003etheoretical physics\u003c\/strong\u003e, and \u003cstrong\u003edifferential geometry\u003c\/strong\u003e, and serves as the most comprehensive and authoritative source on the subject of Lie groups and algebras.\u003c\/p\u003e","brand":"Springer-Verlag","offers":[{"title":"Default Title","offer_id":49911399481648,"sku":"Sarat_9783540688518","price":6300.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0690\/9968\/4144\/files\/springer-verlag-book-default-title-lie-groups-and-lie-algebras-chapters-7-9-elements-of-mathematics-41209275810096.jpg?v=1775963856","url":"https:\/\/www.retailmaharaj.com\/bn\/products\/lie-groups-and-lie-algebras-chapters-7-9-elements-of-mathematics","provider":"Retail Maharaj","version":"1.0","type":"link"}