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100   $a20080410d2009      uy             0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 14$aThe structure of affine buildings$b[electronic resource] /$fRichard M. Weiss
205   $aCourse Book
210   $aPrinceton, N.J. $cPrinceton University Press$dc2009
215   $a1 online resource (381 p.)
225 1 $aAnnals of mathematics studies ;$vno. 168
300   $aDescription based upon print version of record.
311   $a0-691-13659-9 
311   $a0-691-13881-8 
320   $aIncludes bibliographical references and index.
327   $t Frontmatter -- $tContents -- $tPreface -- $tChapter 1. Affine Coxeter Diagrams -- $tChapter 2. Root Systems -- $tChapter 3. Root Data with Valuation -- $tChapter 4. Sectors -- $tChapter 5. Faces -- $tChapter 6. Gems -- $tChapter 7. Affine Buildings -- $tChapter 8. The Building at Infinity -- $tChapter 9. Trees with Valuation -- $tChapter 10. Wall Trees -- $tChapter 11. Panel Trees -- $tChapter 12. Tree-Preserving Isomorphisms -- $tChapter 13. The Moufang Property at Infinity -- $tChapter 14. Existence -- $tChapter 15. Partial Valuations -- $tChapter 16. Bruhat-Tits Theory -- $tChapter 17. Completions -- $tChapter 18. Automorphisms and Residues -- $tChapter 19. Quadrangles of Quadratic Form Type -- $tChapter 20. Quadrangles of Indifferent Type -- $tChapter 21. Quadrangles of Type E6, E7 and E8 -- $tChapter 22. Quadrangles of Type F4 -- $tChapter 23. Quadrangles of Involutory Type -- $tChapter 24. Pseudo-Quadratic Quadrangles -- $tChapter 25. Hexagons -- $tChapter 26. Assorted Conclusions -- $tChapter 27. Summary of the Classification -- $tChapter 28. Locally Finite Bruhat-Tits Buildings -- $tChapter 29. Appendix A -- $tChapter 30. Appendix B -- $tBibliography -- $tIndex
330   $aIn The Structure of Affine Buildings, Richard Weiss gives a detailed presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986. The book includes numerous results about automorphisms, completions, and residues of these buildings. It also includes tables correlating the results in the locally finite case with the results of Tits's classification of absolutely simple algebraic groups defined over a local field. A companion to Weiss's The Structure of Spherical Buildings, The Structure of Affine Buildings is organized around the classification of spherical buildings and their root data as it is carried out in Tits and Weiss's Moufang Polygons.
410  0$aAnnals of mathematics studies ;$vno. 168.
606   $aBuildings (Group theory)
606   $aMoufang loops
606   $aAutomorphisms
606   $aAffine algebraic groups
610   $aAddition.
610   $aAdditive group.
610   $aAdditive inverse.
610   $aAlgebraic group.
610   $aAlgebraic structure.
610   $aAmbient space.
610   $aAssociative property.
610   $aAutomorphism.
610   $aBig O notation.
610   $aBijection.
610   $aBilinear form.
610   $aBounded set (topological vector space).
610   $aBounded set.
610   $aCalculation.
610   $aCardinality.
610   $aCauchy sequence.
610   $aCommutative property.
610   $aComplete graph.
610   $aComplete metric space.
610   $aComposition algebra.
610   $aConnected component (graph theory).
610   $aConsistency.
610   $aContinuous function.
610   $aCoordinate system.
610   $aCorollary.
610   $aCoxeter group.
610   $aCoxeter?Dynkin diagram.
610   $aDiagram (category theory).
610   $aDiameter.
610   $aDimension.
610   $aDiscrete valuation.
610   $aDivision algebra.
610   $aDot product.
610   $aDynkin diagram.
610   $aE6 (mathematics).
610   $aE7 (mathematics).
610   $aE8 (mathematics).
610   $aEmpty set.
610   $aEquipollence (geometry).
610   $aEquivalence class.
610   $aEquivalence relation.
610   $aEuclidean geometry.
610   $aEuclidean space.
610   $aExistential quantification.
610   $aFree monoid.
610   $aFundamental domain.
610   $aHyperplane.
610   $aInfimum and supremum.
610   $aJacques Tits.
610   $aK0.
610   $aLinear combination.
610   $aMathematical induction.
610   $aMetric space.
610   $aMultiple edges.
610   $aMultiplicative inverse.
610   $aNumber theory.
610   $aOctonion.
610   $aParameter.
610   $aPermutation group.
610   $aPermutation.
610   $aPointwise.
610   $aPolygon.
610   $aProjective line.
610   $aQuadratic form.
610   $aQuaternion.
610   $aRemainder.
610   $aRoot datum.
610   $aRoot system.
610   $aScientific notation.
610   $aSphere.
610   $aSubgroup.
610   $aSubring.
610   $aSubset.
610   $aSubstructure.
610   $aTheorem.
610   $aTopology of uniform convergence.
610   $aTopology.
610   $aTorus.
610   $aTree (data structure).
610   $aTree structure.
610   $aTwo-dimensional space.
610   $aUniform continuity.
610   $aValuation (algebra).
610   $aVector space.
610   $aWithout loss of generality.
615  0$aBuildings (Group theory)
615  0$aMoufang loops.
615  0$aAutomorphisms.
615  0$aAffine algebraic groups.
676   $a512/.2
686   $aSI 830$2rvk
700   $aWeiss$b Richard M$g(Richard Mark),$f1946-$01523006
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910780926103321
996   $aThe structure of affine buildings$93836906
997   $aUNINA