Hopf algebras over Chevalley groups
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918386205720576 |
|---|---|
| author | Andruskiewitsch, Nicolás Carnovale, Giovanna |
| author_facet | Andruskiewitsch, Nicolás Carnovale, Giovanna |
| contents | We show that every finite-dimensional pointed Hopf algebra over a finite simple Chevalley group, different from $PSL_2(q)$ with q= 3 mod 4 (and from $PSL_3(2)\simeq PSL_2(7)$), is isomorphic to the corresponding group algebra. To do this, we complete the analysis of the Nichols algebras of Yetter-Drinfeld modules over such groups whose support is a semisimple orbit, begun in arXiv:1506.06794, arXiv:2301.03361. In addition to the techniques used in loc. cit., we introduce a general procedure to determine when a semisimple conjugacy class in a Chevalley or Steinberg group is of type C and a new criterion based on the results of arXiv:2411.02304 that applies to arbitrary racks. Throughout the process, we obtain results on Nichols algebras over racks beyond the framework of Chevalley groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12428 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hopf algebras over Chevalley groups Andruskiewitsch, Nicolás Carnovale, Giovanna Quantum Algebra Group Theory 16T05, 20D06 We show that every finite-dimensional pointed Hopf algebra over a finite simple Chevalley group, different from $PSL_2(q)$ with q= 3 mod 4 (and from $PSL_3(2)\simeq PSL_2(7)$), is isomorphic to the corresponding group algebra. To do this, we complete the analysis of the Nichols algebras of Yetter-Drinfeld modules over such groups whose support is a semisimple orbit, begun in arXiv:1506.06794, arXiv:2301.03361. In addition to the techniques used in loc. cit., we introduce a general procedure to determine when a semisimple conjugacy class in a Chevalley or Steinberg group is of type C and a new criterion based on the results of arXiv:2411.02304 that applies to arbitrary racks. Throughout the process, we obtain results on Nichols algebras over racks beyond the framework of Chevalley groups. |
| title | Hopf algebras over Chevalley groups |
| topic | Quantum Algebra Group Theory 16T05, 20D06 |
| url | https://arxiv.org/abs/2603.12428 |