The structure and representation of \(n\)-ary algebras of DNA recombination
type: Item
instance of: scholarly article
title: The structure and representation of \(n\)-ary algebras of DNA recombination
zbMATH Open document ID: 1252.17016
author: Sergei R. Sverchkov
published in: Central European Journal of Mathematics
publication date: 2011-12-12T00:00:00Z
review text: The paper is devoted to the structure and representation of \(n\)-ary algebras arising from DNA recombination, where \(n\) is the number of DNA segments participating in recombination. The author applies methods which involve a generalization of the Jordan formalization of observables in quantum mechanics in \(n\)-ary splicing algebras. He proves 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 \(3n-2\). This result solves an open problem in the theory of \(n\)-ary intermolecular recombination [\textit{M. R. Bremner}, Discrete Contin. Dyn. Syst., Ser. S 4, No. 6, 1387--1399 (2011; Zbl 1256.17001)].
Mathematics Subject Classification ID: 17C50
Mathematics Subject Classification ID: 17A42
Mathematics Subject Classification ID: 17D92
zbMATH DE Number: 5987917
zbMATH Keywords: Jordan algebras
zbMATH Keywords: DNA recombination
zbMATH Keywords: splicing algebras
zbMATH Keywords: special algebras
reviewed by: Sh. A. Ayupov
MaRDI profile type: Publication
full work available at URL: s11533-011-0087-y
OpenAlex ID: W2159990240
cites work: Jordan algebras arising from intermolecular recombination
cites work: Polynomial identities for ternary intermolecular recombination
cites work: On Homomorphic Images of Special Jordan Algebras
cites work: Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
cites work: Q5732712
cites work: Q4753119
cites work: Q5682023
cites work: Jordan elements in a free associative algebra. I
cites work: Special varieties of Jordan algebras
cites work: Varieties of special algebras
cites work: Q3633604
cites work: Q3947798
DOI: 10.2478/S11533-011-0087-Y
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description: scientific article; zbMATH DE number 5987917