Regular evolution algebras are universally finite

Costoya, Cristina; Ligouras, Panagiote; Tocino, Alicia; Viruel, Antonio

doi:10.1090/proc/15648

Regular evolution algebras are universally finite
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by Cristina Costoya, Panagiote Ligouras, Alicia Tocino and Antonio Viruel PDF

Proc. Amer. Math. Soc. 150 (2022), 919-925 Request permission

Abstract:

In this paper we show that evolution algebras over any given field $\Bbbk$ are universally finite. In other words, given any finite group $G$, there exist infinitely many regular evolution algebras $X$ such that $Aut(X)\cong G$. 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 $\mathbf {G}$ over $\Bbbk$ is isomorphic to the algebraic affine group scheme of automorphisms of a regular evolution algebra.

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