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OverviewThis book explores applications of Jordan theory to the theory of Lie algebras. It begins with the general theory of nonassociative algebras and of Lie algebras and then focuses on properties of Jordan elements of special types. Then it proceeds to the core of the book, in which the author explains how properties of the Jordan algebra attached to a Jordan element of a Lie algebra can be used to reveal properties of the Lie algebra itself. One of the special features of this book is that it carefully explains Zelmanov's seminal results on infinite-dimensional Lie algebras from this point of view. The book is suitable for advanced graduate students and researchers who are interested in learning how Jordan algebras can be used as a powerful tool to understand Lie algebras, including infinite-dimensional Lie algebras. Although the book is on an advanced and rather specialized topic, it spends some time developing necessary introductory material, includes exercises for the reader, and is accessible to a student who has finished their basic graduate courses in algebra and has some familiarity with Lie algebras in an abstract algebraic setting. Full Product DetailsAuthor: Antonio Fernandez LopezPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.738kg ISBN: 9781470450861ISBN 10: 1470450860 Pages: 299 Publication Date: 30 August 2019 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction Nonassociative algebras General facts on Lie algebras Absolute zero divisors Jordan elements von Neumann regular elements Extremal elements A characterization of strong primeness From Lie algebras to Jordan algebras The Kostrikin radical Algebraic Lie algebras and local finiteness From Lie algebras to Jordan pairs An Artinian theory for Lie algebras Inner ideal structure of Lie algebras Classical infinite-dimensional Lie algebras Classical Banach-Lie algebras Bibliography Index of notations IndexReviewsAuthor InformationAntonio Fernandez Lopez, Universidad de Malaga, Spain. Tab Content 6Author Website:Countries AvailableAll regions |
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