Dynkin diagrams and short Peirce gradings of Kantor pairs |
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Authors: | Bruce Allison John Faulkner |
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Institution: | 1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canadaballison@ualberta.ca;3. Department of Mathematics, University of Virginia, Charlottesville, Virgina |
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Abstract: | In a recent article with Oleg Smirnov, we defined short Peirce (SP) graded Kantor pairs. For any such pair P, we defined a family, parameterized by the Weyl group of type BC2, consisting of SP-graded Kantor pairs called Weyl images of P. In this article, we classify finite dimensional simple SP-graded Kantor pairs over an algebraically closed field of characteristic 0 in terms of marked Dynkin diagrams, and we show how to compute Weyl images using these diagrams. The theory is particularly attractive for close-to-Jordan Kantor pairs (which are variations of Freudenthal triple systems), and we construct the reflections of such pairs (with nontrivial gradings) starting from Jordan pairs of matrices. |
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Keywords: | Primary 17B60 17B70 Secondary 17C99 |
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