Abstract:
Using the fact that absolute zero divisors in Jordan pairs become Lie sandwiches of the corresponding Tits–Kantor–Koecher Lie algebras, we prove local nilpotency of the McCrimmon radical of a Jordan system (algebra, triple system, or pair) over an arbitrary ring of scalars. As an application, we show that simple Jordan systems are always nondegenerate.
The first two authors were partially supported by the Spanish Ministerio de Economía y Competitividad and Fondos FEDER, MTM2014-52470-P. The third author was partially supported by the National Science Foundation of the USA.
Citation:
José A. Anquela, Teresa Cortés, Efim Zelmanov, “Local nilpotency of the McCrimmon radical of a Jordan system”, Algebra, geometry, and number theory, Collected papers. Dedicated to Academician Vladimir Petrovich Platonov on the occasion of his 75th birthday, Trudy Mat. Inst. Steklova, 292, MAIK Nauka/Interperiodica, Moscow, 2016, 7–15; Proc. Steklov Inst. Math., 292 (2016), 1–9
\Bibitem{AnqCorZel16}
\by Jos\'e~A.~Anquela, Teresa~Cort\'es, Efim~Zelmanov
\paper Local nilpotency of the McCrimmon radical of a Jordan system
\inbook Algebra, geometry, and number theory
\bookinfo Collected papers. Dedicated to Academician Vladimir Petrovich Platonov on the occasion of his 75th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2016
\vol 292
\pages 7--15
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968516010015}
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\jour Proc. Steklov Inst. Math.
\yr 2016
\vol 292
\pages 1--9
\crossref{https://doi.org/10.1134/S0081543816010016}
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This publication is cited in the following 4 articles: