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Nondegeneracy for Lie Triple Systems and Kantor Pairs

  Published:2011-03-05
 Printed: Sep 2011
  • Esther García,
    Departamento de Matemática Aplicada, Universidad Rey Juan Carlos, 28933 Móstoles (Madrid), Spain
  • Miguel Gómez Lozano,
    Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, 29071 Málaga, Spain
  • Erhard Neher,
    Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N 6N5
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Abstract

We study the transfer of nondegeneracy between Lie triple systems and their standard Lie algebra envelopes as well as between Kantor pairs, their associated Lie triple systems, and their Lie algebra envelopes. We also show that simple Kantor pairs and Lie triple systems in characteristic $0$ are nondegenerate.
Keywords: Kantor pairs, Lie triple systems, Lie algebras Kantor pairs, Lie triple systems, Lie algebras
MSC Classifications: 17A40, 17B60, 17B99 show english descriptions Ternary compositions
Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50]
None of the above, but in this section
17A40 - Ternary compositions
17B60 - Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50]
17B99 - None of the above, but in this section
 

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