Isogeny classes of cubic spaces
arXiv (Cornell University)(2022)
摘要
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.
更多查看译文
关键词
cubic spaces
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要