Jordan Structures in Lie Algebras
Seiten
2019
American Mathematical Society (Verlag)
978-1-4704-5086-1 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-5086-1 (ISBN)
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Explores applications of Jordan theory to the theory of Lie algebras. After presenting the general theory of nonassociative algebras and of Lie algebras, the book then 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.
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.
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.
Antonio Fernandez Lopez, Universidad de Malaga, Spain.
Introduction
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
Index
| Erscheinungsdatum | 02.09.2019 |
|---|---|
| Reihe/Serie | Mathematical Surveys and Monographs |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 738 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-5086-0 / 1470450860 |
| ISBN-13 | 978-1-4704-5086-1 / 9781470450861 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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