The Trajectory Coset and Similarity Classes of Affine Maps
Group Theory
2020-09-15 v1 Commutative Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.2009.05963,
title = {The Trajectory Coset and Similarity Classes of Affine Maps},
author = {Arieh Yakir},
journal= {arXiv preprint arXiv:2009.05963},
year = {2020}
}