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Commutator algebras arising from splicing operations

100%

Sverchkov S.

Open Mathematics

2014

tom 12

nr 11

1687-1699

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.

The structure and representation of n-ary algebras of DNA recombination

100%

Sverchkov S.

Open Mathematics

2011

tom 9

nr 6

1193-1216

In this paper we investigate the structure and representation of n-ary algebras arising from DNA recombination, where n is a number of DNA segments participating in recombination. Our methods involve a generalization of the Jordan formalization of observables in quantum mechanics in n-ary splicing algebras. It is proved that every identity satisfied by n-ary DNA recombination, with no restriction on the degree, is a consequence of n-ary commutativity and a single n-ary identity of the degree 3n-2. It solves the well-known open problem in the theory of n-ary intermolecular recombination.

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2 Open Mathematics

2 Sverchkov S.

1 2014

1 2011

Wyniki wyszukiwania

Commutator algebras arising from splicing operations

The structure and representation of n-ary algebras of DNA recombination