Journal of the Mathematical Society of Japan

Isotropic quadrangular algebras

Bernhard MÜHLHERR and Richard M. WEISS

Advance publication

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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, Advance publication (2019), 60 pages.

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

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, advance publication, 2 July 2019. doi:10.2969/jmsj/80178017. https://projecteuclid.org/euclid.jmsj/1562033194


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