Lie algebras generated by reflections in types BCD
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917461676261376 |
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| author | Drupieski, Christopher M. Kujawa, Jonathan R. |
| author_facet | Drupieski, Christopher M. Kujawa, Jonathan R. |
| contents | We consider the group algebra over the field of complex numbers of the Weyl group of type B (the hyperoctahedral group, or the group of signed permutations) and of the Weyl group of type D (the demihyperoctahedral group, or the group of even-signed permutations), viewed as Lie algebras via the commutator bracket, and determine the structure of the Lie subalgebras generated by the sets of reflections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01198 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lie algebras generated by reflections in types BCD Drupieski, Christopher M. Kujawa, Jonathan R. Representation Theory 17B60, 20F55 We consider the group algebra over the field of complex numbers of the Weyl group of type B (the hyperoctahedral group, or the group of signed permutations) and of the Weyl group of type D (the demihyperoctahedral group, or the group of even-signed permutations), viewed as Lie algebras via the commutator bracket, and determine the structure of the Lie subalgebras generated by the sets of reflections. |
| title | Lie algebras generated by reflections in types BCD |
| topic | Representation Theory 17B60, 20F55 |
| url | https://arxiv.org/abs/2506.01198 |