Groups acting simply transitively on the vertices of a building of type \(\tilde A_ 2\). II: The cases \(q=2\) and \(q=3\)

DOI10.1007/BF01266618zbMath0784.51011OpenAlexW1969278443MaRDI QIDQ685222

Donald I. Cartwright, Tim Steger, Anna Maria Mantero, Anna Zappa

Publication date: 30 September 1993

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01266618

zbMATH Keywords

buildings of type \(\tilde A_ 2\)simply transitively acting groupstriangle presentations

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Finite affine and projective planes (geometric aspects) (51E15) Buildings and the geometry of diagrams (51E24) Linear algebraic groups over local fields and their integers (20G25)

Related Items (21)

Arithmetic structure of CMSZ fake projective planes ⋮ On the Haagerup inequality and groups acting on \(\tilde A_ n\)-buildings ⋮ An Investigation Into the Cyclically Presented Groups with Length Three Positive Relators ⋮ Generalized polygons and star graphs of cyclic presentations of groups ⋮ Proper proximality in non-positive curvature ⋮ Discrete subgroups acting transitively on vertices of a Bruhat-Tits building ⋮ A geometric construction of panel-regular lattices for buildings of types \(\widetilde A_2\) and \(\widetilde C_2\). ⋮ Property (T) discrete quantum groups and subfactors with triangle presentations ⋮ A representation of the chamber set Hecke algebra of an affine building ⋮ A homogeneous \({\tilde{A}}_2\)-building with a non-discrete automorphism group is Bruhat-Tits ⋮ Triangle presentations and tilting modules for \(\operatorname{SL}_{2k+1}\) ⋮ Cohomology of buildings and finiteness properties of ̃𝐴_{𝑛}-groups ⋮ Groups acting simply transitively on vertex sets of hyperbolic triangular buildings ⋮ COCOMPACT ACTIONS ON HYPERBOLIC BUILDINGS ⋮ Some groups whose reduced \(C^*\)-algebra is simple ⋮ Computing Kazhdan Constants by Semidefinite Programming ⋮ A family of \(\widetilde A_n\)-groups ⋮ The strong rigidity theorem for non-Archimedean uniformization ⋮ Formules de Matsushima, de Garland et propriété (T) pour des groupes agissant sur des espaces symétriques ou des immeubles ⋮ Groups acting simply transitively on Ã_n buildings ⋮ Property \((T)\) and \(\widetilde{A}_ 2\) groups

Uses Software

• REDUCE
• MACSYMA

Cites Work

• The affine building of type \(\tilde A_ 2\) over a local field of characteristic two
• The 2-adic affine building of type \(\tilde A_ 2\) and its finite projections
• On density properties of S-subgroups of locally compact groups
• An Algebraic Surface with K Ample, (K 2 ) = 9, p g = q = 0
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