论文标题
仿射图的轨迹固定和相似性类别
The Trajectory Coset and Similarity Classes of Affine Maps
论文作者
论文摘要
在这项工作中，我们定义了仿射图的轨迹余形，并使用它来研究仿射图的相似性类别。我们使用轨迹库，该工具使我们能够更深入地了解几何（仿射图的属性）和代数（线性图的属性）之间的相互作用。我们首先说明了仿射图相似性的几何问题。然后，我们开发代数工具。主要思想是一个不变的发展，该发展决定了在模块的同构之下是否可以将一个固定固定在另一个caset上。解决此问题后，我们回到几何问题，相似性和不变的公寓。
In this work we define the trajectory coset of an affine map and use it to study the similarity classes of affine maps. We use the trajectory coset, a tool which allows us to gain a deeper understanding of the interplay between geometry (properties of affine maps) and algebra (properties of linear maps). We first state the geometric problem of similarity of affine maps. We then develop the algebraic tools. The main idea is the development of an invariant which determines whether one coset can be taken to another coset, under isomorphism of modules. After resolving this problem we go back to geometrical questions, similarity and invariant flats.
