Behavior and dynamics of the set of absolute nilpotent and idempotent elements of chain of evolution algebras depending on the time

TL;DR

This paper constructs families of three-dimensional evolution algebras satisfying Chapman-Kolmogorov equations, analyzing how properties like nilpotent and idempotent elements evolve over time.

Contribution

It introduces specific time-dependent evolution algebra chains and studies their nilpotent and idempotent element dynamics, expanding understanding of algebraic evolution over time.

Findings

Behavior of baric property over time

Dynamics of absolute nilpotent elements

Evolution of idempotent elements

Abstract

In this paper we construct some families of three-dimensional evolution algebras which satisfies Chapman-Kolmogorov equation. For all of these chains we study the behavior of the baric property, the behavior of the set of absolute nilpotent elements and dynamics of the set of idempotent elements depending on the time.