论文标题
常规进化代数是普遍有限的
Regular evolution algebras are universally finite
论文作者
论文摘要
在本文中，我们表明，任何给定字段$ \ bbbk $上的进化代数都是普遍有限的。换句话说，鉴于任何有限的$ g $，存在无限的许多常规进化代数$ x $，因此$ aut（x）\ cong g $。该证明是建立在有限简单（非定向）图的类别到（有限维度）常规进化代数类别的构造的协变忠实函数上的。最后，我们表明，$ \ bbbk $上的任何恒定有限的代数仿射组方案$ \ mathbf {g} $在常规进化代数的自动形态的代数仿射组方案是同构的。
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.
