On Artin groups admitting retractions to parabolic subgroups
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914920773189632 |
|---|---|
| author | de la Cruz, Bruno Aaron Cisneros Cumplido, María Foniqi, Islam |
| author_facet | de la Cruz, Bruno Aaron Cisneros Cumplido, María Foniqi, Islam |
| contents | We generalize the retractions to standard parabolic subgroups for even Artin groups to FC-type Artin groups and other more general families. We prove that these retractions uniquely extend to any parabolic subgroup. We use retractions to generalize the results of Antolín and Foniqi that reduce the problem of intersection of parabolic subgroups to weaker conditions. As a corollary, we characterize coherence for the FC case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12291 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Artin groups admitting retractions to parabolic subgroups de la Cruz, Bruno Aaron Cisneros Cumplido, María Foniqi, Islam Group Theory 20F36, 20F65 (Primary) We generalize the retractions to standard parabolic subgroups for even Artin groups to FC-type Artin groups and other more general families. We prove that these retractions uniquely extend to any parabolic subgroup. We use retractions to generalize the results of Antolín and Foniqi that reduce the problem of intersection of parabolic subgroups to weaker conditions. As a corollary, we characterize coherence for the FC case. |
| title | On Artin groups admitting retractions to parabolic subgroups |
| topic | Group Theory 20F36, 20F65 (Primary) |
| url | https://arxiv.org/abs/2408.12291 |