论文标题
Von Staudt构造，用于偏斜线性和多线性Matroids
Von Staudt Constructions for Skew-Linear and Multilinear Matroids
论文作者
论文摘要
本文比较了偏斜线性和多线性矩阵表示。这些是在分裂环和（大致说）可逆矩阵上代表的矩形。主要工具是von Staudt Construction，我们将问题转化为代数。在对Von Staudt构造的简单变体进行了阐述之后，我们提出以下结果： $ \ bullet $不可证明几个Matroid代表性问题。 $ \ bullet $是具有无限多线性特征集的矩阵的示例，但在特征$ 0 $中不是多线性的。 $ \ bullet $一个不是多线性的偏斜线性矩阵的示例。
This paper compares skew-linear and multilinear matroid representations. These are matroids that are representable over division rings and (roughly speaking) invertible matrices, respectively. The main tool is the von Staudt construction, by which we translate our problems to algebra. After giving an exposition of a simple variant of the von Staudt construction we present the following results: $\bullet$ Undecidability of several matroid representation problems over division rings. $\bullet$ An example of a matroid with an infinite multilinear characteristic set, but which is not multilinear in characteristic $0$. $\bullet$ An example of a skew-linear matroid that is not multilinear.
