The idempotency in the genetic algebras generated by QSO on infinite state space

In this paper, we recall the notion of a quadratic stochastic operator (QSO) generated by a special distribution on infinite state space. Also, we consider the concept of genetic algebras generated by these QSOs. This paper aims to study the idempotency in the genetic algebras generated by QSO and defined by special distributions, including geometric, Poisson, mixture geometric, mixture Poisson and heterogeneous mixture geometric and Poisson distributions