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|a QA252.5
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| 100 |
1 |
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|a López, Antonio Fernández,
|d 1952-
|e author.
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| 245 |
1 |
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|a Jordan structures in Lie algebras /
|c Antonio Fernández López.
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| 264 |
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1 |
|a Providence, Rhode Island :
|b American Mathematical Society,
|c [2019]
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| 264 |
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4 |
|c ©2019
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| 300 |
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|a xi, 299 pages :
|b illustrations ;
|c 26 cm.
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| 336 |
|
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|a text
|b txt
|2 rdacontent
|
| 337 |
|
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|a unmediated
|b n
|2 rdamedia
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| 338 |
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|a volume
|b nc
|2 rdacarrier
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| 490 |
1 |
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|a Mathematical surveys and monographs ;
|v volume 240
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| 504 |
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|a Includes bibliographical references (pages 285-292) and indexes.
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| 505 |
0 |
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|a 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.
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| 520 |
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|a This 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.
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| 650 |
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|a Jordan algebras.
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| 650 |
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|a Lie algebras.
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| 830 |
|
0 |
|a Mathematical surveys and monographs ;
|v no. 240.
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| 907 |
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|a .b29440580
|b 02-11-20
|c 06-19-19
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