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https://doi.org/10.21256/zhaw-1743| Publikationstyp: | Beitrag in wissenschaftlicher Zeitschrift |
| Art der Begutachtung: | Peer review (Publikation) |
| Titel: | Collineations of smooth stable planes |
| Autor/-in: | Bödi, Richard |
| DOI: | 10.21256/zhaw-1743 10.1515/form.10.6.751 |
| Erschienen in: | Forum Mathematicum |
| Band(Heft): | 10 |
| Heft: | 6 |
| Seite(n): | 751 |
| Seiten bis: | 773 |
| Erscheinungsdatum: | 1-Nov-1998 |
| Verlag / Hrsg. Institution: | De Gruyter |
| Verlag / Hrsg. Institution: | de Gruyter |
| ISSN: | 0933-7741 |
| Sprache: | Englisch |
| Fachgebiet (DDC): | 510: Mathematik |
| Zusammenfassung: | Smooth stable planes have been introduced in [4]. We show that every continuous collineation between two smooth stable planes is in fact a smooth collineation. This implies that the group Γ of all continuous collineations of a smooth stable plane is a Lie transformation group on both the set P of points and the set ℒ of lines. In particular, this shows that the point and line sets of a (topological) stable plane ℐ admit at most one smooth structure such that ℐ becomes a smooth stable plane. The investigation of central and axial collineations in the case of (topological) stable planes due to R. Löwen ([25], [26], [27]) is continued for smooth stable planes. Many results of [26] which are only proved for low dimensional planes (dim ℐ ≤ 4) are transferred to smooth stable planes of arbitrary finite dimension. As an application of these transfers we show that the stabilizers Γ[c,c] 1 and Γ[A,A] 1 (see (3.2) Notation) are closed, simply connected, solvable subgroups of Aut(ℐ) (Corollary (4.17)). Moreover, we show that Γ[c,c] is even abelian (Theorem (4.18)). In the closing section we investigate the behaviour of reflections. |
| Weitere Angaben: | Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch) |
| URI: | https://digitalcollection.zhaw.ch/handle/11475/3260 |
| Volltext Version: | Publizierte Version |
| Lizenz (gemäss Verlagsvertrag): | Lizenz gemäss Verlagsvertrag |
| Departement: | School of Engineering |
| Enthalten in den Sammlungen: | Publikationen School of Engineering |
Dateien zu dieser Ressource:
| Datei | Beschreibung | Größe | Format | |
|---|---|---|---|---|
| 1998_Bödi_Collineations of smooth stable planes_Forum Math.pdf | 1.85 MB | Adobe PDF |  Öffnen/Anzeigen |
Zur Langanzeige
Bödi, R. (1998). Collineations of smooth stable planes. Forum Mathematicum, 10(6), 751–773. https://doi.org/10.21256/zhaw-1743
Bödi, R. (1998) ‘Collineations of smooth stable planes’, Forum Mathematicum, 10(6), pp. 751–773. Available at: https://doi.org/10.21256/zhaw-1743.
R. Bödi, “Collineations of smooth stable planes,” Forum Mathematicum, vol. 10, no. 6, pp. 751–773, Nov. 1998, doi: 10.21256/zhaw-1743.
BÖDI, Richard, 1998. Collineations of smooth stable planes. Forum Mathematicum. 1 November 1998. Bd. 10, Nr. 6, S. 751–773. DOI 10.21256/zhaw-1743
Bödi, Richard. 1998. “Collineations of Smooth Stable Planes.” Forum Mathematicum 10 (6): 751–73. https://doi.org/10.21256/zhaw-1743.
Bödi, Richard. “Collineations of Smooth Stable Planes.” Forum Mathematicum, vol. 10, no. 6, Nov. 1998, pp. 751–73, https://doi.org/10.21256/zhaw-1743.
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