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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2206.03779 |
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| _version_ | 1866929347209723904 |
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| author | Rembado, Gabriele |
| author_facet | Rembado, Gabriele |
| contents | We introduce a class of graphs with coloured edges to encode subsystems of the classical root systems, which in particular classify them up to equivalence. We further use the graphs to describe root-kernel intersections, as well as restrictions of root (sub)systems on such intersections, generalising the regular part of a Cartan subalgebra. We also consider a slight variation to encode the hyperplane arrangements only, showing there is a unique noncrystallographic arrangement that arises. Finally, a variation of the main definition leads to elementary classifications of closed and Levi root subsystems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_03779 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A colourful classification of (quasi) root systems and hyperplane arrangements Rembado, Gabriele Rings and Algebras Combinatorics Representation Theory 17B22, 52C35 We introduce a class of graphs with coloured edges to encode subsystems of the classical root systems, which in particular classify them up to equivalence. We further use the graphs to describe root-kernel intersections, as well as restrictions of root (sub)systems on such intersections, generalising the regular part of a Cartan subalgebra. We also consider a slight variation to encode the hyperplane arrangements only, showing there is a unique noncrystallographic arrangement that arises. Finally, a variation of the main definition leads to elementary classifications of closed and Levi root subsystems. |
| title | A colourful classification of (quasi) root systems and hyperplane arrangements |
| topic | Rings and Algebras Combinatorics Representation Theory 17B22, 52C35 |
| url | https://arxiv.org/abs/2206.03779 |