**Memoirs of the American Mathematical Society**

2019;
90 pp;
Softcover

MSC: Primary 16; 20; 17;

**Print ISBN: 978-1-4704-3554-7
Product Code: MEMO/259/1245**

List Price: $81.00

AMS Member Price: $48.60

MAA Member Price: $72.90

**Electronic ISBN: 978-1-4704-5245-2
Product Code: MEMO/259/1245.E**

List Price: $81.00

AMS Member Price: $48.60

MAA Member Price: $72.90

# Moufang Sets and Structurable Division Algebras

Share this page
*Lien Boelaert; Tom De Medts; Anastasia Stavrova*

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

# Table of Contents

## Moufang Sets and Structurable Division Algebras

- Cover Cover11
- Title page i2
- Introduction 18
- Chapter 1. Moufang sets 512
- Chapter 2. Structurable algebras 1926
- Chapter 3. One-invertibility for structurable algebras 3542
- Chapter 4. Simple structurable algebras and simple algebraic groups 4956
- Chapter 5. Moufang sets and structurable division algebras 6976
- Chapter 6. Examples 7986
- 6.1. Associative algebras with involution 7986
- 6.2. Jordan algebras 7986
- 6.3. Hermitian structurable algebras 7986
- 6.4. Structurable algebras of skew-dimension one 8188
- 6.5. Forms of the tensor product of two composition algebras 8592
- 6.6. Classification theorem for structurable division algebras 8693

- Bibliography 8794
- Back Cover Back Cover1102