Geodesic
Weyl Images of Kantor Pairs
Canadian journal of mathematics, Tome 69 (2017) no. 4, pp. 721-766

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DOI

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 ${{\text{E}}_{6}}$ .
DOI : 10.4153/CJM-2016-047-1
Mots-clés : 17B60, 17B70, 17C99, 17B65, Kantor pair, graded Lie algebra, Jordan pair 
Allison, Bruce; Faulkner, John; Smirnov, Oleg. Weyl Images of Kantor Pairs. Canadian journal of mathematics, Tome 69 (2017) no. 4, pp. 721-766. doi: 10.4153/CJM-2016-047-1
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     author = {Allison, Bruce and Faulkner, John and Smirnov, Oleg},
     title = {Weyl {Images} of {Kantor} {Pairs}},
     journal = {Canadian journal of mathematics},
     pages = {721--766},
     year = {2017},
     volume = {69},
     number = {4},
     doi = {10.4153/CJM-2016-047-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2016-047-1/}
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