Monoids generated by projections
Group Theory
2026-03-31 v1
Abstract
We define and explore semireflection monoids on a finite-dimensional vector space. These are monoids generated by semireflections: linear maps fixing a subspace of codimension 1. We mostly focus on the case of projection monoids (where the generating semireflections are non-invertible). After exploring some general theory, we give some important examples, and give classification results for projection monoids on and . We then briefly introduce affine projection monoids.
Cite
@article{arxiv.2603.28500,
title = {Monoids generated by projections},
author = {Matthew Fayers},
journal= {arXiv preprint arXiv:2603.28500},
year = {2026}
}