Genetic Algebras generated by b−bistochastic Quadratic Stochastic Operators: The Character and Associativity

Abstract

In the present paper we consider a genetic algebra induced by b−bistochastic Quadratic Stochastic Operators (QSOs) which is called b−bistochastic genetic algebra. First, we characterize their nontrivial character function on Rn. It turns out that, the given character function is not unique, hence full descriptions of such functions on R1 and R2 are established. Moreover, the defined algebra is commutative but not associative in general, hence, the associativity of b−bistochastic genetic algebras defined on R1 and R2 are described. In this work, the existence of non-trivial derivations on such algebras are given.

Genetic Algebras Associated with ξ(a)-Quadratic Stochastic Operators

“…Remark 2. It is worth mentioning that the characters of Lotka-Volterra and other kinds of genetic algebras have been investigated in [40,44].…”

“…Recently, in [ 38 , 39 , 40 , 41 ], derivations of Lotka–Volterra algebras have been described. Furthermore, other types of genetic algebras have been investigated in [ 42 , 43 , 44 , 45 , 46 , 47 ].…”