eBook ISBN:  9781470404192 
Product Code:  MEMO/173/818.E 
List Price:  $66.00 
MAA Member Price:  $59.40 
AMS Member Price:  $39.60 
eBook ISBN:  9781470404192 
Product Code:  MEMO/173/818.E 
List Price:  $66.00 
MAA Member Price:  $59.40 
AMS Member Price:  $39.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 173; 2005; 99 ppMSC: Primary 51; 16; 20
Very recently, the classification of Moufang polygons has been completed by Tits and Weiss. Moufang \(n\)gons exist for \(n \in \{ 3, 4, 6, 8 \}\) only. For \(n \in \{ 3, 6, 8 \}\), the proof is nicely divided into two parts: first, it is shown that a Moufang \(n\)gon can be parametrized by a certain interesting algebraic structure, and secondly, these algebraic structures are classified. The classification of Moufang quadrangles \((n=4)\) is not organized in this way due to the absence of a suitable algebraic structure. The goal of this article is to present such a uniform algebraic structure for Moufang quadrangles, and to classify these structures without referring back to the original Moufang quadrangles from which they arise, thereby also providing a new proof for the classification of Moufang quadrangles, which does consist of the division into these two parts. We hope that these algebraic structures will prove to be interesting in their own right.
ReadershipGraduate students and research mathematicians interested in algebra and algebraic geometry.

Table of Contents

Chapters

1. Introduction

2. Definition

3. Some identities

4. From quadrangular systems to Moufang quadrangles

5. From Moufang quadrangles to quadrangular systems

6. Some remarks

7. Examples

8. The classification


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Very recently, the classification of Moufang polygons has been completed by Tits and Weiss. Moufang \(n\)gons exist for \(n \in \{ 3, 4, 6, 8 \}\) only. For \(n \in \{ 3, 6, 8 \}\), the proof is nicely divided into two parts: first, it is shown that a Moufang \(n\)gon can be parametrized by a certain interesting algebraic structure, and secondly, these algebraic structures are classified. The classification of Moufang quadrangles \((n=4)\) is not organized in this way due to the absence of a suitable algebraic structure. The goal of this article is to present such a uniform algebraic structure for Moufang quadrangles, and to classify these structures without referring back to the original Moufang quadrangles from which they arise, thereby also providing a new proof for the classification of Moufang quadrangles, which does consist of the division into these two parts. We hope that these algebraic structures will prove to be interesting in their own right.
Graduate students and research mathematicians interested in algebra and algebraic geometry.

Chapters

1. Introduction

2. Definition

3. Some identities

4. From quadrangular systems to Moufang quadrangles

5. From Moufang quadrangles to quadrangular systems

6. Some remarks

7. Examples

8. The classification