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# Weyl Images of Kantor Pairs

Published:2017-04-20
Printed: Aug 2017
• Bruce Allison,
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
• John Faulkner,
Department of Mathematics, University of Virginia, Kerchof Hall, P.O. Box 400137, Charlottesville VA 22904-4137 USA
• Oleg Smirnov,
Department of Mathematics, College of Charleston, Charleston, SC, USA 29424-0001
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## Abstract

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 them to Lie algebras graded by the root system of type $\mathrm{BC}_2$. 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 $\mathrm{E}_6$.
 Keywords: Kantor pair, graded Lie algebra, Jordan pair
 MSC Classifications: 17B60 - Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50] 17B70 - Graded Lie (super)algebras 17C99 - None of the above, but in this section 17B65 - Infinite-dimensional Lie (super)algebras [See also 22E65]

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