Higher Dimensional Analogues of the Modular and Picard Groups

DOI10.2307/2001009zbMath0673.20022OpenAlexW4249503670MaRDI QIDQ3826749

Norbert J. Wielenberg, P. L. Waterman, Colin Maclachlan

Publication date: 1989

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2001009

zbMATH Keywords

Clifford algebraarithmetic groupshyperbolic isometriesClifford groupgraph amalgamation productgroup generated by reflectionsby hyperbolic elementsmodular group PSL(2,\({\mathbb{Z}})\)of vertex groupsorbit of infinityPicard group PSL(2,\({\mathbb{Z}}(i))\)points fixedpoints fixed by parabolic elements

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Functions of hypercomplex variables and generalized variables (30G35) Discrete subgroups of Lie groups (22E40) Structure of modular groups and generalizations; arithmetic groups (11F06) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Clifford algebras, spinors (15A66) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40)

Related Items (6)

A dichotomy for integral group rings via higher modular groups as amalgamated products ⋮ Quaternionic Kleinian modular groups and arithmetic hyperbolic orbifolds over the quaternions ⋮ The covolume of discrete subgroups of \(\mathrm{Iso}(\mathbb H^{2m})\) ⋮ Prescribing the behaviour of geodesics in negative curvature ⋮ Ideal Uniform Polyhedra in and Covolumes of Higher Dimensional Modular Groups ⋮ Farey polytopes and continued fractions associated with discrete hyperbolic groups

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