Presenting the Zassenhaus Lie algebra by the Magnus Lie algebra
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915622845153280 |
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| author | Marmo, Ettore Riley, David Weigel, Thomas |
| author_facet | Marmo, Ettore Riley, David Weigel, Thomas |
| contents | It is shown that the Zassenhaus restricted $\mathbb F_p$-Lie algebra of a (pro-p) group G can be presented by the Magnus Lie algebra of G. For the class of (pro-p) groups for which the terms of the lower central series are torsion-free, the Zassenhaus restricted $\mathbb F_p$-Lie algebra can be explicitly computed from the Magnus Lie algebra. These results apply to orientable surface groups, right-angled Artin groups, pure braid groups, fundamental groups of supersolvable hyperplane arrangements and fundamental groups of strictly supersolvable toric arrangements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13379 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Presenting the Zassenhaus Lie algebra by the Magnus Lie algebra Marmo, Ettore Riley, David Weigel, Thomas Group Theory 20F40 (Primary) 17B70, 20F14 (Secondary) It is shown that the Zassenhaus restricted $\mathbb F_p$-Lie algebra of a (pro-p) group G can be presented by the Magnus Lie algebra of G. For the class of (pro-p) groups for which the terms of the lower central series are torsion-free, the Zassenhaus restricted $\mathbb F_p$-Lie algebra can be explicitly computed from the Magnus Lie algebra. These results apply to orientable surface groups, right-angled Artin groups, pure braid groups, fundamental groups of supersolvable hyperplane arrangements and fundamental groups of strictly supersolvable toric arrangements. |
| title | Presenting the Zassenhaus Lie algebra by the Magnus Lie algebra |
| topic | Group Theory 20F40 (Primary) 17B70, 20F14 (Secondary) |
| url | https://arxiv.org/abs/2511.13379 |