Please use this identifier to cite or link to this item:
https://doi.org/10.21256/zhaw-1743
Publication type: | Article in scientific journal |
Type of review: | Peer review (publication) |
Title: | Collineations of smooth stable planes |
Authors: | Bödi, Richard |
DOI: | 10.21256/zhaw-1743 10.1515/form.10.6.751 |
Published in: | Forum Mathematicum |
Volume(Issue): | 10 |
Issue: | 6 |
Page(s): | 751 |
Pages to: | 773 |
Issue Date: | 1-Nov-1998 |
Publisher / Ed. Institution: | De Gruyter |
Publisher / Ed. Institution: | de Gruyter |
ISSN: | 0933-7741 |
Language: | English |
Subject (DDC): | 510: Mathematics |
Abstract: | 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. |
Further description: | Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch) |
URI: | https://digitalcollection.zhaw.ch/handle/11475/3260 |
Fulltext version: | Published version |
License (according to publishing contract): | Licence according to publishing contract |
Departement: | School of Engineering |
Appears in collections: | Publikationen School of Engineering |
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1998_Bödi_Collineations of smooth stable planes_Forum Math.pdf | 1.85 MB | Adobe PDF | View/Open |
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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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