论文标题
超双重张量的空间
Ultrahomogeneous tensor 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。使用分类的fraïssé理论，我们表明有一个通用的超双重立方体空间$ v $可计数无限维度，这是唯一的同构。 $ v $的自动形态组$ g $非常大，在某些方面，类似于无限正交组。我们表明，$ g $是一个线性 - 拟象化群体（我们介绍的一类组），我们确定$ g $的代数表示理论。我们还建立了一些关于$ v $的模型理论结果：它是$ω$ - 分类的（从修改的意义上），并且具有量化器消除（对于向量）。我们的结果不是特定于立方空间的特定，并且可容纳非常一般的张量空间。我们将这些空间视为模型理论中研究的关系结构的线性类似物。
A cubic space is a vector space equipped with a symmetric trilinear form. Using categorical Fraïssé theory, we show that there is a universal ultrahomogeneous cubic space $V$ of countable infinite dimension, which is unique up to isomorphism. The automorphism group $G$ of $V$ is quite large and, in some respects, similar to the infinite orthogonal group. We show that $G$ is a linear-oligomorphic group (a class of groups we introduce), and we determine the algebraic representation theory of $G$. We also establish some model-theoretic results about $V$: it is $ω$-categorical (in a modified sense), and has quantifier elimination (for vectors). Our results are not specific to cubic spaces, and hold for a very general class of tensor spaces; we view these spaces as linear analogs of the relational structures studied in model theory.
