Antisymetric matrices and Lotka-Volterra algebras

TL;DR

This paper investigates the structure of Lotka-Volterra algebras, focusing on their idempotent elements and automorphisms, by analyzing their defining antisymmetric matrices in relation to biological interaction models.

Contribution

It provides a detailed structural analysis of Lotka-Volterra algebras, highlighting their automorphisms and idempotent elements based on antisymmetric matrices, a novel approach in this context.

Findings

Characterization of idempotent elements in Lotka-Volterra algebras

Description of automorphism groups of these algebras

Connection established between algebraic structure and biological models

Abstract

The purpose of this paper is to study the structure of Lotka-Volterra algebras, the set of their idempotent elements and their group of automorphisms. These algebras are defined through antisymmetric matrices and they emerge in connection with biological problems and Lotka-Volterra systems for the interactions of neighboring individuals.