LEADER 08404nam 2201849 450 001 9910797524903321 005 20200520144314.0 010 $a1-4008-7401-7 024 7 $a10.1515/9781400874019 035 $a(CKB)3710000000478197 035 $a(SSID)ssj0001522021 035 $a(PQKBManifestationID)12640759 035 $a(PQKBTitleCode)TC0001522021 035 $a(PQKBWorkID)11456043 035 $a(PQKB)10961762 035 $a(StDuBDS)EDZ0001756489 035 $a(DE-B1597)460048 035 $a(OCoLC)1023996695 035 $a(OCoLC)1029823322 035 $a(OCoLC)979624924 035 $a(DE-B1597)9781400874019 035 $a(Au-PeEL)EBL2028336 035 $a(CaPaEBR)ebr11080905 035 $a(CaONFJC)MIL815477 035 $a(OCoLC)939554323 035 $a(MiAaPQ)EBC2028336 035 $a(EXLCZ)993710000000478197 100 $a20150303d2015 uy| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDescent in buildings /$fBernhard Mu?hlherr, Holger P. Petersson, and Richard M. Weiss 210 1$aPrinceton :$cPrinceton University Press,$d2015. 215 $a1 online resource (353 pages) $cillustrations 225 1 $aAnnals of mathematics studies ;$v190 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-691-16691-9 311 $a0-691-16690-0 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tContents -- $tPreface -- $tPART 1. Moufang Quadrangles -- $tChapter 1. Buildings -- $tChapter 2. Quadratic Forms -- $tChapter 3. Moufang Polygons -- $tChapter 4. Moufang Quadrangles -- $tChapter 5. Linked Tori, I -- $tChapter 6. Linked Tori, II -- $tChapter 7. Quadratic Forms over a Local Field -- $tChapter 8. Quadratic Forms of Type E6, E7 and E8 -- $tChapter 9. Quadratic Forms of Type F4 -- $tPART 2. Residues in Bruhat-Tits Buildings -- $tChapter 10. Residues -- $tChapter 11. Unramified Quadrangles of Type E6, E7 and E8 -- $tChapter 12. Semi-ramified Quadrangles of Type E6, E7 and E8 -- $tChapter 13. Ramified Quadrangles of Type E6, E7 and E8 -- $tChapter 14. Quadrangles of Type E6, E7 and E8: Summary -- $tChapter 15. Totally Wild Quadratic Forms of Type E7 -- $tChapter 16. Existence -- $tChapter 17. Quadrangles of Type F4 -- $tChapter 18. The Other Bruhat-Tits Buildings -- $tPART 3. Descent -- $tChapter 19. Coxeter Groups -- $tChapter 20. Tits Indices -- $tChapter 21. Parallel Residues -- $tChapter 22. Fixed Point Buildings -- $tChapter 23. Subbuildings -- $tChapter 24. Moufang Structures -- $tChapter 25. Fixed Apartments -- $tChapter 26. The Standard Metric -- $tChapter 27. Affine Fixed Point Buildings -- $tPART 4. Galois Involutions -- $tChapter 28. Pseudo-Split Buildings -- $tChapter 29. Linear Automorphisms -- $tChapter 30. Strictly Semi-linear Automorphisms -- $tChapter 31. Galois Involutions -- $tChapter 32. Unramified Galois Involutions -- $tPART 5. Exceptional Tits Indices -- $tChapter 33. Residually Pseudo-Split Buildings -- $tChapter 34. Forms of Residually Pseudo-Split Buildings -- $tChapter 35. Orthogonal Buildings -- $tChapter 36. Indices for the Exceptional Bruhat-Tits Buildings -- $tBibliography -- $tIndex 330 $aDescent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fixed by a group to form a kind of subbuilding or "form" of the original building. At the center of this theory is the notion of a Tits index, a combinatorial version of the notion of an index in the relative theory of algebraic groups. These results are combined at the end to show that every exceptional Bruhat-Tits building arises as a form of a "residually pseudo-split" Bruhat-Tits building. The book concludes with a display of the Tits indices associated with each of these exceptional forms.This is the third and final volume of a trilogy that began with Richard Weiss' The Structure of Spherical Buildings and The Structure of Affine Buildings. 410 0$aAnnals of mathematics studies ;$v190. 606 $aBuildings (Group theory) 606 $aCombinatorial geometry 610 $aBruhat-Tits building. 610 $aClifford invariant. 610 $aCoxeter diagram. 610 $aCoxeter group. 610 $aCoxeter system. 610 $aEuclidean plane. 610 $aFundamental Theorem of Descent. 610 $aMoufang building. 610 $aMoufang condition. 610 $aMoufang polygon. 610 $aMoufang quadrangle. 610 $aMoufang set. 610 $aMoufang structure. 610 $aPfister form. 610 $aStructure Theorem. 610 $aTits index. 610 $aabelian group. 610 $aabsolute Coxeter diagram. 610 $aabsolute Coxeter system. 610 $aabsolute rank. 610 $aaffine building. 610 $aalgebraic group. 610 $aanisotropic pseudo-quadratic space. 610 $aanisotropic quadratic space. 610 $aanti-isomorphism. 610 $aapartment. 610 $aarctic region. 610 $aautomorphism. 610 $abilinear form. 610 $abiquaternion division algebra. 610 $abuilding. 610 $acanonical isomorphism. 610 $achamber. 610 $acompatible representation. 610 $adescent group. 610 $adescent. 610 $adiscrete valuation. 610 $aexceptional Moufang quadrangle. 610 $aexceptional quadrangle. 610 $afinite dimension. 610 $afixed point building. 610 $afixed point theory. 610 $agem. 610 $ageneralized quadrangle. 610 $ahyperbolic plane. 610 $ahyperbolic quadratic module. 610 $ahyperbolic quadratic space. 610 $ainvolutory set. 610 $aisomorphism. 610 $aisotropic quadratic space. 610 $alength function. 610 $anon-abelian group. 610 $aparallel residues. 610 $apolar space. 610 $aprojection map. 610 $aproper indifferent set. 610 $aproper involutory set. 610 $apseudo-quadratic space. 610 $apseudo-split building. 610 $aquadratic form. 610 $aquadratic module. 610 $aquadratic space. 610 $aquaternion division algebra. 610 $aramified quadrangle. 610 $aramified quaternion division algebra. 610 $aramified separable quadratic extension. 610 $arelative Coxeter diagram. 610 $arelative Coxeter group. 610 $arelative Coxeter system. 610 $arelative rank. 610 $aresidual quadratic spaces. 610 $aresidue. 610 $aroot group sequence. 610 $aroot. 610 $around quadratic space. 610 $ascalar multiplication. 610 $asemi-ramified quadrangle. 610 $aseparable quadratic extension. 610 $asimplicial complex. 610 $aspecial vertex. 610 $aspherical building. 610 $asplit quadratic space. 610 $astandard involution. 610 $asubbuilding of split type. 610 $asubbuilding. 610 $atamely ramified division algebra. 610 $athick building. 610 $athin T-building. 610 $atrace map. 610 $atrace. 610 $aunramified quadrangle. 610 $aunramified quadratic space. 610 $aunramified quaternion division algebra. 610 $aunramified separable quadratic extension. 610 $avector space. 610 $avertex. 610 $aweak isomorphism. 610 $awild quadratic space. 615 0$aBuildings (Group theory) 615 0$aCombinatorial geometry. 676 $a516/.13 700 $aMu?hlherr$b Bernhard Matthias$01472122 702 $aPetersson$b Holger P.$f1939- 702 $aWeiss$b Richard M$g(Richard Mark),$f1946- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910797524903321 996 $aDescent in buildings$93684795 997 $aUNINA