The structure over \(\mathbb{Z}[q,q^{-1}]\) of Hecke orders of dihedral groups

DOI10.1006/jabr.1999.8060zbMath0955.16020OpenAlexW2087330041MaRDI QIDQ1975154

Klaus W. Roggenkamp

Publication date: 27 November 2000

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1999.8060

zbMATH Keywords

function fieldsalgebraic number fieldsirreducible representationsdihedral groupsHecke ordersmodular representationsintegral affine schemesirreducible closed subschemes

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Representations of orders, lattices, algebras over commutative rings (16G30) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05)

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On the generation gap of a finite group, Classification of the Auslander-Reiten quivers of local Gorenstein orders and a characterization of the simple curve singularities, Zur Einheitengruppe der ganzzahligen Gruppenringe metazyklischer Frobeniusgruppen, Lower K-theory of nilpotent groups, On Bass orders, The cell structure, the Brauer tree structure, and extensions of cell modules for Hecke orders of dihedral groups, Which integral group rings are Bass orders?, Integral representations of a certain twisted group ring, Zeta functions and integral representation theory, Free presentations and relation modules of finite groups, Injective modules for group rings and Gorenstein orders, Automorphisms and nonabelian cohomology: An algorithm, On orders and multiple fibre products, Local crossed-product orders of finite representation type

Cites Work

• Higher-dimensional orders, graph-orders, and derived equivalences
• Cellular algebras
• Blocks with cyclic defect of Hecke orders of Coxeter groups
• Blocks of cyclic defect and green-orders
• The cell structure, the Brauer tree structure, and extensions of cell modules for Hecke orders of dihedral groups
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