Monoids generated by projections
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914431703711744 |
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| author | Fayers, Matthew |
| author_facet | Fayers, Matthew |
| contents | 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 $\mathbb C^2$ and $\mathbb R^3$. We then briefly introduce affine projection monoids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28500 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monoids generated by projections Fayers, Matthew Group Theory 15A99, 20F55, 20M99 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 $\mathbb C^2$ and $\mathbb R^3$. We then briefly introduce affine projection monoids. |
| title | Monoids generated by projections |
| topic | Group Theory 15A99, 20F55, 20M99 |
| url | https://arxiv.org/abs/2603.28500 |