New Properties for Markov Evolution Algebras

Resumen

Evolution algebras are a class of non-associative algebras that arise as a mathematical model to represent non-Mendelian genetics. They have sparked great interest in various fields of knowledge such as graph theory, dynamical systems, and Markov chains. The concept was first introduced by [4], in a finite-dimensional approach, and later extended by [3]. In this work, we review the properties established by [3] and, by exploring their connection with Probability Theory, simplify some of the proofs. In addition, we extend some results and establish new properties for the case where Λ is not finite. Theorem 1 formalizes how a Markov evolution algebra is associated with a given discrete-time Markov chain (X_n)_n≥0, provided that transition probability conditions hold. Once this connection is well-established, certain properties can be derived by exploring the relationship between Markov chains and evolution algebras. [...]