Cargando…
Grassmannians of classical buildings /
Buildings are combinatorial constructions successfully exploited to study groups of various types. The vertex set of a building can be naturally decomposed into subsets called Grassmannians. The book contains both classical and more recent results on Grassmannians of buildings of classical types. It...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, NJ :
World Scientific,
©2010.
|
| Colección: | Algebra and discrete mathematics (World Scientific (Firm)) ;
v. 2. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1. Linear algebra and projective geometry. 1.1. Vector spaces. 1.2. Projective spaces. 1.3. Semilinear mappings. 1.4. Fundamental theorem of projective geometry. 1.5. Reflexive forms and polarities
- 2. Buildings and Grassmannians. 2.1. Simplicial complexes. 2.2. Coxeter systems and Coxeter complexes. 2.3. Buildings. 2.4. Mappings of Grassmannians
- 3. Classical Grassmannians. 3.1. Elementary properties of Grassmann spaces. 3.2. Collineations of Grassmann spaces. 3.3. Apartments. 3.4. Apartments preserving mappings. 3.5. Grassmannians of exchange spaces. 3.6. Matrix geometry and spine spaces. 3.7. Geometry of linear involutions. 3.8. Grassmannians of infinite-dimensional vector spaces
- 4. Polar and half-spin Grassmannians. 4.1. Polar spaces. 4.2. Grassmannians. 4.3. Examples. 4.4. Polar buildings. 4.5. Elementary properties of Grassmann spaces. 4.6. Collineations. 4.7. Opposite relation. 4.8. Apartments. 4.9. Apartments preserving mappings.