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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 Kantor pair, graded Lie algebra, Jordan pair
MSC Classifications: 17B60, 17B70, 17C99, 17B65 show english descriptions Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50]
Graded Lie (super)algebras
None of the above, but in this section
Infinite-dimensional Lie (super)algebras [See also 22E65]
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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