Evolution algebras and graphs

Alberto Elduque; Alicia Labra

Evolution algebras and graphs

Rings and Algebras 2013-12-18 v1

Authors: Alberto Elduque , Alicia Labra

Abstract

A digraph is attached to any evolution algebra. This graph leads to some new purely algebraic results on this class of algebras and allows for some new natural proofs of known results. Nilpotency of an evolution algebra will be proved to be equivalent to the nonexistence of oriented cycles in the graph. Besides, the automorphism group of any evolution algebra $E$ with $E=E^2$ will be shown to be always finite.

Keywords

algebra classification and gradings finite-dimensional algebras automorphism groups

Cite

@article{arxiv.1312.4685,
  title  = {Evolution algebras and graphs},
  author = {Alberto Elduque and Alicia Labra},
  journal= {arXiv preprint arXiv:1312.4685},
  year   = {2013}
}

Comments

10 pages

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