Logo of Humboldt-Universität zu BerlinLogo of Humboldt-Universität zu Berlin
edoc-Server
Open-Access-Publikationsserver der Humboldt-Universität
de|en
Header image: facade of Humboldt-Universität zu Berlin
View Item 
  • edoc-Server Home
  • Artikel und Monographien
  • Zweitveröffentlichungen
  • View Item
  • edoc-Server Home
  • Artikel und Monographien
  • Zweitveröffentlichungen
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.
All of edoc-ServerCommunity & CollectionTitleAuthorSubjectThis CollectionTitleAuthorSubject
PublishLoginRegisterHelp
StatisticsView Usage Statistics
All of edoc-ServerCommunity & CollectionTitleAuthorSubjectThis CollectionTitleAuthorSubject
PublishLoginRegisterHelp
StatisticsView Usage Statistics
View Item 
  • edoc-Server Home
  • Artikel und Monographien
  • Zweitveröffentlichungen
  • View Item
  • edoc-Server Home
  • Artikel und Monographien
  • Zweitveröffentlichungen
  • View Item
2009-10-01Zeitschriftenartikel DOI: 10.1515/ADVGEOM.2009.028
Polarities of shift planes
Knarr, Norbert
Stroppel, Markus
We construct polarities for arbitrary shift planes and develop criteria for conjugacy under the normalizer of the shift group. Under suitable assumptions (in particular, for finite or compact planes) we construct all shift groups on a given plane, and our constructions yield all conjugacy classes of polarities. We show that a translation plane admits an orthogonal polarity if, and only if, it is a shift plane. The corresponding planes are exactly those that can be coordinatized by commutative semifields. The orthogonal polarities form a single conjugacy class. Finally, we construct examples of compact connected shift planes with more conjugacy classes of polarities than the corresponding classical planes.
Files in this item
Thumbnail
advgeom.2009.028.pdf — Adobe PDF — 284.2 Kb
MD5: 85adc9a147cd1f45cce1d8d022259909
Cite
BibTeX
EndNote
RIS
InCopyright
Details
DINI-Zertifikat 2019OpenAIRE validatedORCID Consortium
Imprint Policy Contact Data Privacy Statement
A service of University Library and Computer and Media Service
© Humboldt-Universität zu Berlin
 
DOI
10.1515/ADVGEOM.2009.028
Permanent URL
https://doi.org/10.1515/ADVGEOM.2009.028
HTML
<a href="https://doi.org/10.1515/ADVGEOM.2009.028">https://doi.org/10.1515/ADVGEOM.2009.028</a>