On formal deformations and degenerations of evolution algebras

TL;DR

This paper investigates the formal deformations and degenerations of evolution algebras, classifying their structures and relations, especially focusing on nilpotent cases up to four dimensions.

Contribution

It provides a classification of formal deformations and degenerations of evolution algebras, including Hasse diagrams for nilpotent cases up to four dimensions.

Findings

Classification of formal deformations of evolution algebras.

Hasse diagrams illustrating degeneration relations among nilpotent evolution algebras.

Results applicable to evolution algebras of dimension up to four.

Abstract

The main purpose of this paper is to study formal deformations of evolution algebras, determining their existence and classifying them up to equivalence. In addition, we examine degenerations in this setting and provide Hasse diagrams that describe the degeneration relations among nilpotent evolution algebras of dimensions up to four.