论文标题
序言协助寻找新的简单谎言代数
A Prolog assisted search for new simple Lie algebras
论文作者
论文摘要
我们描述了一些最近的计算机调查，其中包括“有限域的约束逻辑编程” - clp（fd） - 序言编程环境中的库，以搜索$ 2 $元素的$ \ gf（2）$ elements $ \ gf（2）$。由Grishkov等人的论文动机。 al。，我们专门寻找具有“薄分解”的人，我们解决了他们的一种猜想。我们从结果中推断出存在两个新的无限谎言代数的新家族，除了在Dimension中找到七个新的零星例子$ 31 $。我们还更好地将一些先前发现的简单代数的上下文化，将它们置于文献中似乎从未出现过的家庭，并提供了当前已知的人的更新表。
We describe some recent computer investigations with the `Constraint Logic Programming over Finite Domains' -- CLP(FD) -- library in the Prolog programming environment to search for new simple Lie algebras over the field $\GF(2)$ of $2$ elements. Motivated by a paper of Grishkov et. al., we specifically look for those with a `thin decomposition', and we settle one of their conjectures. We extrapolate from our results the existence of two new infinite families of simple Lie algebras, in addition to finding seven new sporadic examples in dimension $31$. We also better contextualise some previously discovered simple algebras, putting them into families which do not seem to have ever appeared in the literature, and give an updated table of those currently known.
