# Volterra Evolution Algebras and Their Graphs

## TL;DR

This paper introduces Volterra evolution algebras characterized by skew symmetric matrices, exploring their properties and linking them to ergodic behaviors of Volterra quadratic stochastic operators.

## Contribution

It establishes a connection between Volterra evolution algebras and ergodicities of Volterra quadratic stochastic operators, and studies their properties like nilpotency and derivations.

## Key findings

- Connection between Volterra evolution algebras and ergodicities established
- Properties such as nilpotency and derivations analyzed
- Structural matrices described by skew symmetric matrices

## 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.