LEADER 03367nam 2200601Ia 450 001 9910438139703321 005 20200520144314.0 010 $a1-299-33555-1 010 $a3-642-34453-4 024 7 $a10.1007/978-3-642-34453-4 035 $a(CKB)2670000000328012 035 $a(EBL)1082808 035 $a(OCoLC)827212400 035 $a(SSID)ssj0000859726 035 $a(PQKBManifestationID)11429569 035 $a(PQKBTitleCode)TC0000859726 035 $a(PQKBWorkID)10882438 035 $a(PQKB)10783029 035 $a(DE-He213)978-3-642-34453-4 035 $a(MiAaPQ)EBC1082808 035 $a(PPN)168326949 035 $a(EXLCZ)992670000000328012 100 $a20100125d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDiagram geometry $erelated to classical groups and buildings /$fFrancis Buekenhout, Arjeh M. Cohen 205 $a1st ed. 2013. 210 $aBerlin ;$aHeidelberg $cSpringer-Verlag$d2013 215 $a1 online resource (595 p.) 225 0 $aErgebnisse der mathematik und ihrer grenzgebiete. 3. folge / a series of modern surveys in mathematics ;$v57 300 $aDescription based upon print version of record. 311 $a3-642-44226-9 311 $a3-642-34452-6 327 $a1. Geometries -- 2. Diagrams -- 3. Chamber Systems -- 4. Thin Geometries -- 5. Linear Geometries -- 6. Projective and Affine Spaces -- 7. Polar Spaces -- 8. Projective Embeddings of Polar Spaces -- 9. Embedding Polar Spaces in Absolutes -- 10. Classical Polar Spaces -- 11. Buildings -- Bibliography -- Index. 330 $aThis book provides a self-contained introduction to diagram geometry.  Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective. Projective and affine geometry are main examples.  Polar geometry is motivated by polarities on diagram geometries and the complete classification of those polar geometries whose projective planes are Desarguesian is given. It differs from Tits' comprehensive treatment in that it uses Veldkamp's embeddings. The book intends to be a basic reference for those who study diagram geometry.  Group theorists will find examples of the use of diagram geometry.  Light on matroid theory is shed from the point of view of geometry with linear diagrams.  Those interested in Coxeter groups and those interested in buildings will find brief but self-contained introductions into these topics from the diagrammatic perspective.  Graph theorists will find many highly regular graphs. The text is written so graduate students will be able to follow the arguments without needing recourse to further literature. A strong point of the book is the density of examples.  . 410 0$aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x0071-1136 ;$v57 606 $aFinite geometries 606 $aGeometry 615 0$aFinite geometries. 615 0$aGeometry. 676 $a516.12 700 $aBuekenhout$b Francis$060643 701 $aCohen$b Arjeh M$042267 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438139703321 996 $aDiagram geometry$9837214 997 $aUNINA