English

Regular evolution algebras are universally finite

Rings and Algebras 2021-12-15 v3

Abstract

In this paper we show that evolution algebras over any given field k\Bbbk are universally finite. In other words, given any finite group GG, there exist infinitely many regular evolution algebras XX such that Aut(X)GAut(X)\cong G. The proof is built upon the construction of a covariant faithful functor from the category of finite simple (non oriented) graphs to the category of (finite dimensional) regular evolution algebras. Finally, we show that any constant finite algebraic affine group scheme G\mathbf{G} over k\Bbbk is isomorphic to the algebraic affine group scheme of automorphisms of a regular evolution algebra.

Keywords

Cite

@article{arxiv.2002.03338,
  title  = {Regular evolution algebras are universally finite},
  author = {Cristina Costoya and Panagiote Ligouras and Alicia Tocino and Antonio Viruel},
  journal= {arXiv preprint arXiv:2002.03338},
  year   = {2021}
}

Comments

Minor corrections. Bibliography updated. To appear in Proc. Amer. Math. Soc

R2 v1 2026-06-23T13:35:38.736Z