论文标题
域上的二维完美进化代数
Two dimensional perfect evolution algebras over domains
论文作者
论文摘要
我们将研究Evolution代数$ a $，它是尺寸$ 2 $的免费模块。此外，我们将假设这些代数是完美的，即$ a^2 = a $。首先，我们对代数对域进行了一些一般考虑：它们夹在某个必需的$ d $ -subModule及其标量扩展之间。我们介绍了Quasiperfect代数的概念，并在\ cite {elduquegraphs}中给出的字段上稍微修改了将图与进化代数相关联的过程。本质上，我们在连接箭头中引入颜色，具体取决于与自然基础元素平方相关的合适标准。然后，我们通过方便模量在范围参数化同构类别的范围参数下对代数进行了分类。
We will study evolution algebras $A$ which are free modules of dimension $2$ over domains. Furthermore, we will assume that these algebras are perfect, that is $A^2=A$. We start by making some general considerations about algebras over domains: they are sandwiched between a certain essential $D$-submodule and its scalar extension over the field of fractions of the domain. We introduce the notion of quasiperfect algebras and modify slightly the procedure to associate a graph to an evolution algebra over a field given in \cite{ElduqueGraphs}. Essentially, we introduce color in the connecting arrows, depending on a suitable criterion related to the squares of the natural basis elements. Then we classify the algebras under scope parametrizing the isomorphic classes by convenient moduli.
