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Softcover ISBN:  9781470435547 
Product Code:  MEMO/259/1245 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
eBook ISBN:  9781470452452 
Product Code:  MEMO/259/1245.E 
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MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
Softcover ISBN:  9781470435547 
eBook ISBN:  9781470452452 
Product Code:  MEMO/259/1245.B 
List Price:  $162.00 $121.50 
MAA Member Price:  $145.80 $109.35 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 259; 2019; 90 ppMSC: Primary 16; 20; 17
A Moufang set is essentially a doubly transitive permutation group such that each point stabilizer contains a normal subgroup which is regular on the remaining vertices; these regular normal subgroups are called the root groups, and they are assumed to be conjugate and to generate the whole group.
It has been known for some time that every Jordan division algebra gives rise to a Moufang set with abelian root groups. The authors extend this result by showing that every structurable division algebra gives rise to a Moufang set, and conversely, they show that every Moufang set arising from a simple linear algebraic group of relative rank one over an arbitrary field \(k\) of characteristic different from \(2\) and \(3\) arises from a structurable division algebra.
The authors also obtain explicit formulas for the root groups, the \(\tau\)map and the Hua maps of these Moufang sets. This is particularly useful for the Moufang sets arising from exceptional linear algebraic groups.

Table of Contents

Chapters

Introduction

1. Moufang sets

2. Structurable algebras

3. Oneinvertibility for structurable algebras

4. Simple structurable algebras and simple algebraic groups

5. Moufang sets and structurable division algebras

6. Examples


Additional Material

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A Moufang set is essentially a doubly transitive permutation group such that each point stabilizer contains a normal subgroup which is regular on the remaining vertices; these regular normal subgroups are called the root groups, and they are assumed to be conjugate and to generate the whole group.
It has been known for some time that every Jordan division algebra gives rise to a Moufang set with abelian root groups. The authors extend this result by showing that every structurable division algebra gives rise to a Moufang set, and conversely, they show that every Moufang set arising from a simple linear algebraic group of relative rank one over an arbitrary field \(k\) of characteristic different from \(2\) and \(3\) arises from a structurable division algebra.
The authors also obtain explicit formulas for the root groups, the \(\tau\)map and the Hua maps of these Moufang sets. This is particularly useful for the Moufang sets arising from exceptional linear algebraic groups.

Chapters

Introduction

1. Moufang sets

2. Structurable algebras

3. Oneinvertibility for structurable algebras

4. Simple structurable algebras and simple algebraic groups

5. Moufang sets and structurable division algebras

6. Examples