Hilbert evolution algebras and its connection with discrete-time Markov chains

TL;DR

This paper extends the concept of evolution algebras to infinite-dimensional Hilbert spaces and explores their connection with discrete-time Markov chains on countable state spaces.

Contribution

It introduces a Hilbert space framework for evolution algebras, enabling analysis of infinite-dimensional cases and linking them to Markov chain theory.

Findings

Established a Hilbert space extension of evolution algebras.

Connected infinite-dimensional evolution algebras with discrete-time Markov chains.

Provided examples illustrating the applicability of the framework.

Abstract

Evolution algebras are non-associative algebras. In this work we provide an extension of this class of algebras, in the context of Hilbert spaces, capable to deal with infinite-dimensional spaces. We illustrate the applicability of our approach by discussing a connection with discrete-time Markov chains with countable state space.