## Journal of the Mathematical Society of Japan

- J. Math. Soc. Japan
- Volume 71, Number 4 (2019), 1321-1380.

### Isotropic quadrangular algebras

Bernhard MÜHLHERR and Richard M. WEISS

#### Abstract

Quadrangular algebras arise in the theory of Tits quadrangles. They are anisotropic if and only if the corresponding Tits quadrangle is, in fact, a Moufang quadrangle. Anisotropic quadrangular algebras were classified in the course of classifying Moufang polygons. In this paper we extend the classification of anisotropic quadrangular algebras to a classification of isotropic quadrangular algebras satisfying a natural non-degeneracy condition.

#### Note

The work of the first author was partially supported by a grant from the DFG and the work of the second author was partially supported by a collaboration grant from the Simons Foundation.

#### Article information

**Source**

J. Math. Soc. Japan, Volume 71, Number 4 (2019), 1321-1380.

**Dates**

Received: 19 March 2018

Revised: 19 August 2018

First available in Project Euclid: 2 July 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.jmsj/1562033194

**Digital Object Identifier**

doi:10.2969/jmsj/80178017

**Mathematical Reviews number (MathSciNet)**

MR4023310

**Zentralblatt MATH identifier**

07174409

**Subjects**

Primary: 17D99: None of the above, but in this section

Secondary: 20E42: Groups with a $BN$-pair; buildings [See also 51E24] 51E12: Generalized quadrangles, generalized polygons 51E24: Buildings and the geometry of diagrams

**Keywords**

building Tits polygon quadrangular algebra

#### Citation

MÜHLHERR, Bernhard; WEISS, Richard M. Isotropic quadrangular algebras. J. Math. Soc. Japan 71 (2019), no. 4, 1321--1380. doi:10.2969/jmsj/80178017. https://projecteuclid.org/euclid.jmsj/1562033194