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 are universally finite. In other words, given any finite group , there exist infinitely many regular evolution algebras such that . 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 over is isomorphic to the algebraic affine group scheme of automorphisms of a regular evolution algebra.
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