# Commutator algebras arising from splicing operations

Open Mathematics (2014)

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

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topSergei 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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