The structure and representation of \(n\)-ary algebras of DNA recombination
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)].
scientific article; zbMATH DE number 5987917
scientific article