论文标题
在二和三的简单进化代数上。构建简单和半圣经的进化代数
On simple evolution algebras of dimension two and three. Constructing simple and semisimple evolution algebras
论文作者
论文摘要
这项工作将三维简单进化代数分类。为此，我们使用诸如关联的有向图，模量集，电感限制组，Zariski拓扑结构和对角子空间的尺寸之类的工具。明确地，在三维情况下，我们构建了一些模型$ _i \ Mathbf {iii} _ {λ_1，\ ldots，λ_n}^{p，q} $ a此代数的$，带有$ 1 \ le i \ le i \ le i \ le i \ le 4 $，$λ_i\ in \ mathbbbbbbbbbb = $ p，q \ in \ mathbb {n} $，使得任何代数对模型中的一个（和一个）是同构的，我们进一步研究了每个代数的同构问题。此外，我们展示了如何从较小尺寸的已知简单进化代数中构造高阶的简单进化代数。
This work classifies three-dimensional simple evolution algebras over arbitrary fields. For this purpose, we use tools such as the associated directed graph, the moduli set, inductive limit group, Zariski topology and the dimension of the diagonal subspace. Explicitly, in the three-dimensional case, we construct some models $_i\mathbf{III}_{λ_1,\ldots,λ_n}^{p,q}$ of such algebras with $1\le i\le 4$, $λ_i\in\mathbb{K}^\times$, $p,q\in\mathbb{N}$, such that any algebra is isomorphic to one (and only one) of the given in the models and we further investigate the isomorphic question within each one. Moreover, we show how to construct simple evolution algebras of higher-order from known simple evolution algebras of smaller size.
