Hardcover ISBN:  9781470450861 
Product Code:  SURV/240 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470453626 
Product Code:  SURV/240.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9781470450861 
eBook: ISBN:  9781470453626 
Product Code:  SURV/240.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 
Hardcover ISBN:  9781470450861 
Product Code:  SURV/240 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470453626 
Product Code:  SURV/240.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9781470450861 
eBook ISBN:  9781470453626 
Product Code:  SURV/240.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 240; 2019; 299 ppMSC: Primary 17
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 infinitedimensional 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 infinitedimensional 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.
ReadershipGraduate students and researchers interested in algebra.

Table of Contents

Chapters

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 infinitedimensional Lie algebras

Classical Banach–Lie algebras


Additional Material

Reviews

The author has made a real effort to make this material as accessible as possible to an audience of nonspecialists. The definitions of Lie algebras and Jordan algebras are provided, rather than assumed, and early chapters provide background information. These chapters are written at what I would estimate to be the level of a second or third year graduate student; obviously a oneyear graduate algebra course is a prerequisite for the book, and some prior exposure to Lie algebras would be useful as well. The book is written in the style of a textbook rather than a research monograph; it even comes complete with exercises. For somebody contemplating entering this area, this book should prove very valuable.
Mark Hunacek, Iowa State University, MAA Reviews


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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 infinitedimensional 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 infinitedimensional 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.
Graduate students and researchers interested in algebra.

Chapters

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 infinitedimensional Lie algebras

Classical Banach–Lie algebras

The author has made a real effort to make this material as accessible as possible to an audience of nonspecialists. The definitions of Lie algebras and Jordan algebras are provided, rather than assumed, and early chapters provide background information. These chapters are written at what I would estimate to be the level of a second or third year graduate student; obviously a oneyear graduate algebra course is a prerequisite for the book, and some prior exposure to Lie algebras would be useful as well. The book is written in the style of a textbook rather than a research monograph; it even comes complete with exercises. For somebody contemplating entering this area, this book should prove very valuable.
Mark Hunacek, Iowa State University, MAA Reviews