On a class of evolution algebras of ``chicken'' population (Q2925301)

Genetic algebras are the formal language of abstract algebra to model and study inheritance in Genetics and were introduced by \textit{I. M. H. Etherington} [Proc. R. Soc. Edinb. 59, 242--258 (1939; Zbl 0027.29402)].NEWLINENEWLINEGiven an algebra \(A\) and a basis \(\{ e_1, e_2, \dots \}\), their multiplication table is determined by the cubic matrix of structural constants \(\{ \gamma^k_{ij} \}\), where \(e_ie_j = \sum_k \gamma^k_{ij} e_k\). The diversity of such algebras makes their classification into a difficult problem, although some evolution algebras allow simpler matrices, and thus, further analysis and deeper results.NEWLINENEWLINEIn this paper, the authors focus on a very particular class of genetic algebras: evolution algebras of a ``chicken'' population (EACP), which have a basis \(\{ h_1, \dots, h_n, r \}\) in which the structure matrix is rectangular of size \(n \times (n+1)\). \textit{A. Labra}, \textit{M. Ladra} and \textit{U. A. Rozikov} showed in 2014 [Linear Algebra Appl. 457, 348--362 (2014; Zbl 1292.17030)] that EACP are commutative (and hence, flexible), non-associative and not necessarily power-associative, among other properties.NEWLINENEWLINEThis paper continues the study of EACP over the field of complex numbers, providing some structural results, including simpler forms of the multiplication table, which allows for isomorphism theorems in some particular cases. A complete classification of three-dimensional complex EAC is also given.