Artículos de revistas
An evolution algebra in population genetics
Fecha
2014Registro en:
Linear Algebra and Its Applications, Volumen 457,
00243795
10.1016/j.laa.2014.05.036
Autor
Labra, A.
Ladra, M.
Rozikov, U. A.
Institución
Resumen
We consider an evolution algebra which corresponds to a bisexual population with a set of females partitioned into finitely many different types and the males having only one type. We study basic properties of the algebra. This algebra is commutative (and hence flexible), not associative and not necessarily power-associative, in general. We prove that being alternative is equivalent to being associative. We find conditions to be an associative, a fourth power-associative, or a nilpotent algebra. We also prove that if the algebra is not alternative then to be power-associative is equivalent to be Jordan. Moreover it is not unital. In a general case, we describe the full set of idempotent elements and the full set of absolute nilpotent elements. The set of all operators of left (right) multiplications is described. Under some conditions it is proved that the corresponding algebra is centroidal. Moreover the classification of 2-dimensional and some 3-dimensional algebras are obtained. © 2