Journal of the Mathematical Society of Japan

Isotropic quadrangular algebras

Bernhard MÜHLHERR and Richard M. WEISS

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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.


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

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

Received: 19 March 2018
Revised: 19 August 2018
First available in Project Euclid: 2 July 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

building Tits polygon quadrangular algebra


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

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