Imbedding Lie Algebras in Strongly Prime Algebras

Anquela, José A.; Cortés, Teresa

doi:10.1080/00927872.2012.660257

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Proposition 521

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Cited by 2 publications

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“…Because of (11) and (20), we can apply (6) to obtain that I bc+cb ⊆ P and I bd+db ⊆ P . Therefore, (21) yields b, [c, d] , I ⊆ P , which readily implies [c, d] , I ⊆ P , and this is impossible by primeness of P .…”

Section: Proposition 52mentioning

confidence: 99%

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Prime Quotients of Jordan Systems and Lie Algebras

et al. 2015

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We show that, unlike alternative algebras, prime quotients of a nondegenerate Jordan system or a Lie algebra need not be nondegenerate, even if the original Jordan system is primitive, or the Lie algebra is strongly prime, both with nonzero simple hearts. Nevertheless, for Jordan systems and Lie algebras directly linked to associative systems, we prove that even semiprime quotients are necessarily nondegenerate.Mathematics Subject Classification. 16W10, 17C10, 17B05.

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Section: Proposition 52mentioning

confidence: 99%

“…Similar examples of Lie algebras can be obtained using the free Lie algebra. The constructions given in [6,9] are used to show the existence of primitive Jordan systems and strongly prime Lie algebras, both with simple nondegenerate hearts, that have prime degenerate quotients nevertheless.…”

Section: Introductionmentioning

confidence: 99%