Academic Bibliography
https://biblio.ugent.be/
Ghent University Academic Bibliography2000-01-01T00:00+00:001monthlyPoint-line spaces related to Jordan pairs
https://biblio.ugent.be/publication/711106
De Medts, TomMüllherr, BernhardHuggenberger, Simon2009A point-line space is an abstract geometric object that consists of a set of points and a set of lines such that on each line there are at least two points. A large class of point-line spaces with high symmetry comes along with buildings, combinatorial objects that are introduced by Jacques Tits and help to study algebraic objects with geometric methods.
To formulate quantum mechanics as abstract and general as possible, the physicist Pascual Jordan invented a non-associative algebraic structure which is now called Jordan algebra. A generalisation of Jordan algebras are the so-called Jordan pairs. In 1975, Ottmar Loos classified all Jordan pairs with finite dimension. As a matter of fact, the list of Ottmar Loos matches in a certain way a part of the list of types of buildings given by Jacques Tits.
The buildings of the types that correspond to the types of the Jordan pairs provide a class of point-line spaces. This class consists of two exceptional types and an infinite number of types that occur in four series of increasing dimension. There is a natural way to enlarge these series to the cases of infinite dimension. Together with the two exceptional types this is the class of point-line spaces that we consider to be the point-line spaces related to Jordan pairs of arbitrary dimension. The present work gives a characterisation of point-line spaces that determines exactly this class and uses four rather simple axioms. Moreover, we give a full classification of the point-line spaces satisfying these axioms and prove that it is the class mentioned above.application/pdfhttps://biblio.ugent.be/publication/711106http://hdl.handle.net/1854/LU-711106https://biblio.ugent.be/publication/711106/file/4335016engGhent University. Faculty of SciencesNo license (in copyright)info:eu-repo/semantics/openAccessMathematics and StatisticsPoint-line spaces related to Jordan pairsdissertationinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/publishedVersionGrassmannians of arbitrary rank
https://biblio.ugent.be/publication/1256019
Huggenberger, Simon2016We introduce a generalization of Grassmannians of projective spaces that allows us to consider subspaces of any (possibly infinite) rank as points of the Grassmannian. We show that the spaces that we obtain, carry in a natural way the structure of a twin building.application/pdfhttps://biblio.ugent.be/publication/1256019http://hdl.handle.net/1854/LU-1256019https://biblio.ugent.be/publication/1256019/file/1256022engNo license (in copyright)info:eu-repo/semantics/restrictedAccessBULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVINISSN: 1370-1444Mathematics and StatisticsGrassmannians of arbitrary rankjournalArticleinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionDual polar spaces of arbitrary rank
https://biblio.ugent.be/publication/1255874
Huggenberger, Simon2011In 1982 P. Cameron gave a characterisation of dual polar spaces of finite rank viewed as point-line spaces. This characterisation makes essential use of the fact that dual polar spaces of finite rank have finite diameter. Our goal is to give a characterisation which includes dual polar spaces of infinite rank. Since dual polar spaces of infinite rank are disconnected, we introduce a point-relation that denotes pairs of points at "maximal distance", and we call this an opposition relation. This approach is in the spirit of the theory of twin buildings.application/pdfhttps://biblio.ugent.be/publication/1255874http://hdl.handle.net/1854/LU-1255874http://dx.doi.org/10.1515/ADVGEOM.2011.018https://biblio.ugent.be/publication/1255874/file/2097472engNo license (in copyright)info:eu-repo/semantics/openAccessADVANCES IN GEOMETRYISSN: 1615-715XMathematics and StatisticsDual polar spaces of arbitrary rankjournalArticleinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion