Volterra Evolution Algebras and Their Graphs

Abstract

In this paper, we introduce Volterra evolution algebras which are evolution algebras whose structural matrices are described by skew symmetric matrices. A main result of the present paper gives a connection between such kind of algebras with ergodicities of Volterra quadratic stochastic operators. Furthermore, some of properties of the considered algebras such as nilpotency, derivations have been studied as well.