scientific article; zbMATH DE number 194825

Publication date: 5 June 1993

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

finite simple groups Moufang buildings Moufang polygons Coxeter group BN-pair affine building chamber systems Coxeter complexes Lie type groups buildings of spherical type Tits diagrams

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Geometric group theory (20F65) Simple groups: alternating groups and groups of Lie type (20D06) Other finite nonlinear geometries (51E25) Research exposition (monographs, survey articles) pertaining to geometry (51-02) Research exposition (monographs, survey articles) pertaining to group theory (20-02)

Related Items

Factor and normal subgroup theorems for lattices in products of groups, Rigidity of invariant convex sets in symmetric spaces, On closures of orbits and arithmetic of quaternions, Finiteness properties of Chevalley groups over $\mathbb{F}_ q[t$], Finiteness properties of soluble arithmetic groups over global function fields., Random walk on a building of type $\tilde A_r$ and Brownian motion of the Weyl chamber, Minimal supports of geometric cycle codes, Actions of Cartan subgroups, Isomorphisms of Kac-Moody groups which preserve bounded subgroups., Spherical harmonic analysis on affine buildings, Flag-homogeneous compact connected polygons, On homomorphisms between generalized polygons, Generalized polygons with highly transitive collineation groups, Aperiodic tilings, Isospectral Cayley graphs of some finite simple groups, Littlewood-Paley theory for triangle buildings, On generalized projective spaces operating on sets, Commensurability and separability of quasiconvex subgroups., Local to global structure in twin buildings, Cycles in the chamber homology of $\text{GL}(3)$, On the Haagerup inequality and groups acting on $\tilde A_ n$-buildings, On the set of covolumes of lattices for Fuchsian buildings., Weighted $L^2$-cohomology of Coxeter groups., On exchange properties for Coxeter matroids and oriented matroids, Abels's groups revisited., Embedding theorems for non-positively curved polygons of finite groups, Homological stability for classical groups., Minimal paths between maximal chains in finite rank semimodular lattices, Semimodular lattices and semibuildings, Automorphisms of graph-universal Coxeter groups, Root shadow spaces, Characterization of some subgraphs of point-collinearity graphs of building geometries, Translation generalized quadrangles, On panel-regular $\tilde{A}_2$ lattices, Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings, Curtis-Tits groups generalizing Kac-Moody groups of type $\widetilde A_{n-1}$., Partial orders generalizing the weak order on Coxeter groups, Saturated fusion systems with parabolic families., Stability inequalities and universal Schubert calculus of rank 2, Polar manifolds and actions, Hyperbolic Kac-Moody Weyl groups, billiard tables and actions of lattices on buildings., Extremal elements in Coxeter groups and metric commensurators of Kac-Moody groups, Right-angularity, flag complexes, asphericity, Highest weight modules and polarized embeddings of shadow spaces, Leonard pairs from 24 points of view., Vertex opposition in spherical buildings, A geometric construction of panel-regular lattices for buildings of types $\widetilde A_2$ and $\widetilde C_2$., Asymptotic classes of finite Moufang polygons, Combinatorial and group-theoretic compactifications of buildings, Codistances of 3-spherical buildings, Lattices in complete rank 2 Kac-Moody groups., Property (T) discrete quantum groups and subfactors with triangle presentations, Removing chambers in Bruhat-Tits buildings, The flat closing problem for buildings, A classification of flag-transitive classical $c.C_ 2$-geometries by means of generators and relations, Affine buildings for dihedral groups, A `non-additive' characterization of $\wp$-adic norms., A representation of the chamber set Hecke algebra of an affine building, Eigenspaces of operator algebras on the fundamental apartment of an affine building, A geometric construction of generalized quadrangles from polar spaces of rank three, Boundary behavior of generalized Poisson integrals on buildings of type $\widetilde{A}_2$, Clifford algebras and polar planes, Groups acting simply transitively on the vertices of a building of type $\tilde A_ 2$. I, Groups acting simply transitively on the vertices of a building of type $\tilde A_ 2$. II: The cases $q=2$ and $q=3$, Non-discrete affine buildings and convexity, Intersections of apartments, Existence of quasi-periodic triangular buildings, Invariant operators on certain affine buildings of rank 2, Saturated simplicial complexes, Explicit constructions of Ramanujan complexes of type $\widetilde A_d$., LS galleries, the path model, and MV cycles, Connectivity of chamber graphs of buildings and related complexes, Embedding orders into central simple algebras, Asymptotic cones of finitely presented groups, Quadrangles embedded in metasymplectic spaces, Kac-Moody groups, hovels and Littelmann paths, Property A and affine buildings, Intrinsic reflections in Coxeter systems, On finite Moufang polygons, An essay on the Ree octagons, A Curtis-Tits-Phan theorem for the twin-building of type $A_{n-1}$, Simplicity and superrigidity of twin building lattices., Coxeter-Davis lattices and commensurators, Spanning point-line geometries in buildings of spherical type, Actions of the face monoid associated to a Kac-Moody group on its building, A family of $\widetilde A_n$-groups, Buildings have finite asymptotic dimension., Simple groups of finite Morley rank and Tits buildings, Polarized and homogeneous embeddings of dual polar spaces, Simple purely infinite $C^*$-algebras and $n$-filling actions, Combinatorial flag varieties, An adjacency criterion for Coxeter matroids, Eigenfunctions of the Laplace operators for a building of type $\tilde A_2$, Connectedness of opposite-flag geometries in Moufang polygons, Metric characterizations of spherical and Euclidean buildings, Coxeter--Petrie complexes of regular maps, Metric building exercises, Walls in Coxeter complexes, Combinatorial modulus on boundary of right-angled hyperbolic buildings, Property $(T)$ and $\widetilde{A}_ 2$ groups, The 4-string braid group $B_4$ has property RD and exponential mesoscopic rank, Rigidity of skew-angled Coxeter groups, Boundary behaviour of Poisson integrals on buildings of type Ã2, FIXED POINT RATIOS IN EXCEPTIONAL GROUPS OF RANK AT MOST TWO, Isotropic random walks on affine buildings, A free subgroup in the image of the 4-strand Burau representation, Explicit construction of a Ramanujan $(n_1,n_2,\dots,n_{d-1})$-regular hypergraph, 2-dimensional Coxeter groups are biautomatic, Polygons in buildings and their refined side lengths, Chimney retractions in affine buildings encode orbits in affine flag varieties, Affine buildings: construction by norms and study of isometries, Commensurability of lattices in right-angled buildings, Generalization of the Macdonald formula for Hall-Littlewood polynomials, Local selectivity of orders in central simple algebras, Coarse equivalences of Euclidean buildings. (With an appendix by Jeroen Schillewaert and Koen Struyve.), Eigenvalues of the Vertex Set Hecke Algebra of an Affine Building, Cohomology of buildings and finiteness properties of ̃𝐴_{𝑛}-groups, Some infinite groups generated by involutions have Kazhdan's property (T), Sur les immeubles triangulaires et leurs automorphismes, A survey of the additive eigenvalue problem (with Appendix by M. Kapovich), Isomorphisms of Kac-Moody groups, Buildings and Hecke algebras., Moufang planes. Ruth Moufang and her contribution to the foundation of geometry, Representations of matroids in semimodular lattices, Asymptotic Cones and Ultrapowers of Lie Groups, Regular path systems and (bi)automatic groups., Thin buildings., Exotic triangular Tits buildings, Quotients of buildings by groups acting freely on chambers, Triangles of Groups, On the Steinberg-presentation for Lie-type groups, Two-transitive Lie groups, Buildings as Inner Ideal Geometries, Quasi-isometric rigidity of a class of right-angled Coxeter groups, Coxeter Groups act on CAT(0) cube complexes, A Hodge theory for Alexandrov spaces with curvature bounded from above, STRONG SINGULARITY FOR SUBALGEBRAS OF FINITE FACTORS, Symplectic structure on colorings, Lagrangian tangles and Tits buildings, A topological characterization of the Moufang property for compact polygons, Quantitative aspects of acyclicity, Integrability of induction cocycles for Kac-Moody groups, The arithmetic and combinatorics of buildings for 𝑆𝑝_{𝑛}, Group-theoretic compactification of Bruhat–Tits buildings, Buildings and s-Transitive Graphs, Enumerating A₃(2) Blueprints, and an Application, Abelian subgroups of two‐dimensional Artin groups