Group actions and automorphisms of evolution algebras associated to finite graphs

2025/05/21 by Mary Luz Rodiño Montoya, Montoya, Mary Luz Rodiño, Natalia A. Viana Bedoya +3
Computer Science · Mathematics · #05C81 (Secondary) #05E18 (Primary) 05C25 #17A36 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2505.15604

openalex publication_date 2025/05/21 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

Given an evolution algebra associated to a connected finite graph Γ, we exhibit a free action of the group of symmetries of Γ on the set of automorphisms of the algebra. This allows us to explicitly describe this set and we prove that a sufficient condition for it to be finite is that every automorphism is induced by a graph symmetry. Consequently, we extend a known result about perfect evolution algebras to other families.

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• Evolution algebras and graphs
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