Commutator algebras arising from splicing operations

Sergei Sverchkov

Open Mathematics (2014)

  • Volume: 12, Issue: 11, page 1687-1699
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Sergei Sverchkov. "Commutator algebras arising from splicing operations." Open Mathematics 12.11 (2014): 1687-1699. <http://eudml.org/doc/269594>.

@article{SergeiSverchkov2014,
abstract = {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.},
author = {Sergei Sverchkov},
journal = {Open Mathematics},
keywords = {Lie algebras; Algebraic formalization of DNA recombination; Splicing algebras; Varieties of algebras; algebraic formalization of DNA recombination; splicing algebras; varieties of algebras},
language = {eng},
number = {11},
pages = {1687-1699},
title = {Commutator algebras arising from splicing operations},
url = {http://eudml.org/doc/269594},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Sergei Sverchkov
TI - Commutator algebras arising from splicing operations
JO - Open Mathematics
PY - 2014
VL - 12
IS - 11
SP - 1687
EP - 1699
AB - 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.
LA - eng
KW - Lie algebras; Algebraic formalization of DNA recombination; Splicing algebras; Varieties of algebras; algebraic formalization of DNA recombination; splicing algebras; varieties of algebras
UR - http://eudml.org/doc/269594
ER -

References

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  12. [12] Pãun Gh., Rozenberg G, Salomaa A., Computing by splicing, Theoretical Computer Science, 1996, 161, 321–336 http://dx.doi.org/10.1016/S0304-3975(96)00082-5 Zbl0874.68117
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  15. [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 Zbl1196.17024
  16. [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 Zbl1252.17016
  17. [17] Zhevlakov K., Slinko A., Shestakov I., Shirshov A., Rings That Are Nearly Associative, AcademicPress, New York, 1982 Zbl0487.17001

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