Isogeny classes of cubic spaces
Publisher DOI
Abstract
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 . In N ∪ {∞} particular, the set of classes is discrete and (under the partial order of embedability) satisfies the descending chain condition.
Date Issued
2025
Publication Type
Article
Subject(s)
Language(s)
en
Author(s)
Snowden, Andrew |
Additional Credits
Journal
Selecta Mathematica (New Series)
Publisher
Springer
ISSN
1022-1824
1420-9020
Access(Rights)
open.access