Principal bundles over a smooth real projective curve of genus zero
| Autor: | Indranil Biswas, Johannes Huisman |
|---|---|
| Rok vydání: | 2008 |
| Předmět: |
Discrete mathematics
Weil restriction Linear algebraic group Endomorphism Generator (category theory) Principal homogeneous space Reductive group Principal bundle Combinatorics Line bundle ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Geometry and Topology GeneralLiterature_REFERENCE(e.g. dictionaries encyclopedias glossaries) ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | advg. 8:451-472 |
| ISSN: | 1615-7168 1615-715X |
| DOI: | 10.1515/advgeom.2008.029 |
| Popis: | Let H 0 denote the kernel of the endomorphism, defined by , of the real algebraic group given by the Weil restriction of . Let X be a nondegenerate anisotropic conic in . The principal -bundle over the complexification defined by the ample generator of Pic(), gives a principal H 0-bundle over X through a reduction of structure group. Given any principal G-bundle EG over X, where G is any connected reductive linear algebraic group defined over ℝ, we prove that there is a homomorphism such that EG is isomorphic to the principal G-bundle obtained by extending the structure group of using . The tautological line bundle over the real projective line and the principal -bundle together give a principal -bundle F on , Given any principal G-bundle EG over , where G is any connected reductive linear algebraic group defined over ℝ, we prove that there is a homomorphism such that EG is isomorphic to the principal G-bundle obtained by extending the structure group of F using . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|