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2014 | 12 | 11 | 1687-1699
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Commutator algebras arising from splicing operations

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EN
Abstrakty
EN
We prove that the variety of Lie algebras arising from splicing operation coincides with the variety CM of centreby-metabelian Lie algebras. Using these Lie algebras we find the minimal dimension algebras generated the variety CM and the variety of its associative envelope algebras. We study the splicing n-ary operation. We show that all n-ary (n > 2) commutator algebras arising from this operation are nilpotent of index 3. We investigate the generalization of the splicing n-ary operation, and we formulate a series of open problems.
Twórcy
  • Russian Presidential Academy of National Economy and Public Administration, Siberian Branch, SverchkovSR@yandex.ru
Bibliografia
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  • [15] Sverchkov S., Structure and representation of Jordan algebras arising from intermolecular recombination, Contemp. Math., 2009, 483, 261–285 http://dx.doi.org/10.1090/conm/483/09450
  • [16] Sverchkov S., Structure and representations of n-ary algebras of DNA recombination, Cent. Eur. J. Math., 2011, 9(6), 1193–1216 http://dx.doi.org/10.2478/s11533-011-0087-y
  • [17] Zhevlakov K., Slinko A., Shestakov I., Shirshov A., Rings That Are Nearly Associative, AcademicPress, New York, 1982
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-014-0438-6
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