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Weyl Images of Kantor Pairs

Published online by Cambridge University Press:  20 November 2018

Bruce Allison ,
John Faulkner  and
Oleg Smirnov
Bruce Allison
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada e-mail: ballison@ualberta.ca
John Faulkner
Affiliation:
Department of Mathematics, University of Virginia, Kerchof Hall, P.O. Box 400137, Charlottesville, VA, 22904-4137, USA e-mail: jrf@virginia.edu
Oleg Smirnov
Affiliation:
Department of Mathematics, College of Charleston, Charleston, SC, 29424-0001, USA e-mail: smirnov@cofc.edu
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Abstract

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Kantor pairs arise naturally in the study of 5-graded Lie algebras. In this article, we introduce and study Kantor pairs with short Peirce gradings and relate themto Lie algebras graded by the root system of type $\text{B}{{\text{C}}_{2}}$. This relationship allows us to define so-called Weyl images of short Peirce graded Kantor pairs. We use Weyl images to construct new examples of Kantor pairs, including a class of infinite dimensional central simple Kantor pairs over a field of characteristic $\ne$ 2 or 3, as well as a family of forms of a split Kantor pair of type ${{\text{E}}_{6}}$.

Keywords

17B6017B7017C9917B65Kantor pairgraded Lie algebraJordan pair
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 69 , Issue 4 , 01 August 2017 , pp. 721 - 766
Copyright
Copyright © Canadian Mathematical Society 2017

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