论文标题
同类分类的同类空间
Isogeny classes of cubic spaces
论文作者
论文摘要
立方空间是配备对称三线性形式的矢量空间。如果每个立方空间都嵌入另一个，则是同质的。如果不能将其形式表示为线性和二次形式的产物的有限总和，则立方空间是非分类的。我们将可计数维度的非分类立方空间分类为同学：同等类是由我们称为残差等级的不变式确定的，该等级将值在$ \ Mathbf {n} \ cup \ cup \ cup \ {\ infty \} $中。特别是，一组类是离散的，并且（在嵌入性的部分顺序下）满足降链条件。
A cubic space is a vector space equipped with a symmetric trilinear form. Two cubic spaces are isogeneous if each embeds into the other. A cubic space is non-degenerate if its form cannot be expressed as a finite sum of products of linear and quadratic forms. We classify non-degenerate cubic spaces of countable dimension up to isogeny: the isogeny classes are completely determined by an invariant we call the residual rank, which takes values in $\mathbf{N} \cup \{\infty\}$. In particular, the set of classes is discrete and (under the partial order of embedability) satisfies the descending chain condition.
