论文标题
轴向代数的中央延伸
Central extensions of axial algebras
论文作者
论文摘要
在本文中，我们进一步适应了Skjelbred-Sund的方法来构建轴向代数的中心扩展。我们使用我们的方法来证明复杂的简单有限维约旦代数的所有轴向中央延伸（相对于最大轴集）分割，并且所有尺寸$ n \ leq 4 $的非切割轴向中央扩展位于特征性的典型性封闭场上，而不是$ 2 $ jordan。另外，我们给出$ 2 $维轴向代数的分类，并描述这些代数的一些重要属性。
In this article, we develop a further adaptation of the method of Skjelbred-Sund to construct central extensions of axial algebras. We use our method to prove that all axial central extensions (with respect to a maximal set of axes) of complex simple finite-dimensional Jordan algebras are split and that all non-split axial central extensions of dimension $n\leq 4$ over an algebraically closed field of characteristic not $2$ are Jordan. Also, we give a classification of $2$-dimensional axial algebras and describe some important properties of these algebras.
