# Power-associative evolution algebras

## TL;DR

This paper investigates power-associative evolution algebras, providing their Wedderburn decomposition, proving they are Jordan algebras, and classifying them up to dimension six.

## Contribution

It introduces the Wedderburn decomposition for power-associative evolution algebras and classifies these algebras up to dimension six, establishing their Jordan algebra structure.

## Key findings

- Power-associative evolution algebras are Jordan algebras.
- Complete classification of these algebras up to dimension six.
- Explicit Wedderburn decomposition provided.

## Abstract

The paper is devoted to the study of evolution algebras that are power-associative algebras. We give the Wedderburn decomposition of evolution algebras that are power-associative algebras and we prove that these algebras are Jordan algebras. Finally, we use this decomposition to classify these algebras up to dimension six.