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....

The Wells map relates automorphisms with cohomology in the setting of extensions of groups and Lie algebras. We construct the Wells map for some abelian extensions $0\to A\hookrightarrow L\stackrel{\pi }{\to }B\to 0$ of 3-Lie algebras to obtain obstruction classes in $H^1(B,A)$ for a pair of automorphisms in $\mathrm{Aut}\left(A\right)\times \mathrm{Aut}\left(B\right)$ to be inducible from an automorphism of $L$. Application to free nilpotent 3-Lie algebras is discussed.