TY - BOOK ID - 7061521 TI - The Structure of Affine Buildings. (AM-168) PY - 2008 VL - 168 SN - 9780691136592 0691136599 9780691138817 0691138818 9786612458361 1282458361 1400829054 9781400829057 9781282458369 6612458364 PB - Princeton, NJ DB - UniCat KW - Buildings (Group theory) KW - Moufang loops KW - Automorphisms KW - Affine algebraic groups KW - Moufang loops. KW - Automorphisms. KW - Affine algebraic groups. KW - Algebraic groups, Affine KW - Loops, Moufang KW - Theory of buildings (Group theory) KW - Tits's theory of buildings (Group theory) KW - Group schemes (Mathematics) KW - Group theory KW - Symmetry (Mathematics) KW - Loops (Group theory) KW - Linear algebraic groups KW - Buildings (Group theory). KW - Addition. KW - Additive group. KW - Additive inverse. KW - Algebraic group. KW - Algebraic structure. KW - Ambient space. KW - Associative property. KW - Automorphism. KW - Big O notation. KW - Bijection. KW - Bilinear form. KW - Bounded set (topological vector space). KW - Bounded set. KW - Calculation. KW - Cardinality. KW - Cauchy sequence. KW - Commutative property. KW - Complete graph. KW - Complete metric space. KW - Composition algebra. KW - Connected component (graph theory). KW - Consistency. KW - Continuous function. KW - Coordinate system. KW - Corollary. KW - Coxeter group. KW - Coxeter–Dynkin diagram. KW - Diagram (category theory). KW - Diameter. KW - Dimension. KW - Discrete valuation. KW - Division algebra. KW - Dot product. KW - Dynkin diagram. KW - E6 (mathematics). KW - E7 (mathematics). KW - E8 (mathematics). KW - Empty set. KW - Equipollence (geometry). KW - Equivalence class. KW - Equivalence relation. KW - Euclidean geometry. KW - Euclidean space. KW - Existential quantification. KW - Free monoid. KW - Fundamental domain. KW - Hyperplane. KW - Infimum and supremum. KW - Jacques Tits. KW - K0. KW - Linear combination. KW - Mathematical induction. KW - Metric space. KW - Multiple edges. KW - Multiplicative inverse. KW - Number theory. KW - Octonion. KW - Parameter. KW - Permutation group. KW - Permutation. KW - Pointwise. KW - Polygon. KW - Projective line. KW - Quadratic form. KW - Quaternion. KW - Remainder. KW - Root datum. KW - Root system. KW - Scientific notation. KW - Sphere. KW - Subgroup. KW - Subring. KW - Subset. KW - Substructure. KW - Theorem. KW - Topology of uniform convergence. KW - Topology. KW - Torus. KW - Tree (data structure). KW - Tree structure. KW - Two-dimensional space. KW - Uniform continuity. KW - Valuation (algebra). KW - Vector space. KW - Without loss of generality. UR - https://www.unicat.be/uniCat?func=search&query=sysid:7061521 AB - In 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. ER -