Complete reducibility
- In this note, we unify and extend various concepts in the area of \(\it G\)-complete reducibility, where \(\it G\) is a reductive algebraic group. By results of Serre and Bate–Martin–Röhrle, the usual notion of \(\it G\)-complete reducibility can be re-framed as a property of an action of a group on the spherical building of the identity component of \(\it G\). We show that other variations of this notion, such as relative complete reducibility and \(\sigma\)-complete reducibility, can also be viewed as special cases of this building-theoretic definition, and hence a number of results from these areas are special cases of more general properties.
| Author: | Maike Katharina GruchotORCiDGND, Alastair LitterickORCiDGND, Gerhard RöhrleORCiDGND |
|---|---|
| URN: | urn:nbn:de:hbz:294-99743 |
| DOI: | https://doi.org/10.1007/s00229-021-01318-2 |
| Parent Title (English): | Manuscripta mathematica |
| Subtitle (English): | variations on a theme of Serre |
| Publisher: | Springer |
| Place of publication: | Berlin |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2023/06/16 |
| Date of first Publication: | 2021/06/15 |
| Publishing Institution: | Ruhr-Universität Bochum, Universitätsbibliothek |
| Volume: | 168 |
| First Page: | 439 |
| Last Page: | 451 |
| Note: | Dieser Beitrag ist auf Grund des DEAL-Springer-Vertrages frei zugänglich. |
| Dewey Decimal Classification: | Naturwissenschaften und Mathematik / Mathematik |
| open_access (DINI-Set): | open_access |
| faculties: | Fakultät für Mathematik |
| Licence (English): |  Creative Commons - CC BY 4.0 - Attribution 4.0 International |
