An algorithm to compute the primitive central idempotents and the Wedderburn decomposition of a rational group algebra.

DOI10.1016/S0747-7171(03)00035-XzbMath1050.16015OpenAlexW2001308629MaRDI QIDQ1394942

Aurora A. Olivieri, Ángel Del Río

Publication date: 25 June 2003

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0747-7171(03)00035-x

zbMATH Keywords

algorithmsgroup ringsWedderburn decompositionsprimitive central idempotentsprograms

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Group rings (16S34) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Computational aspects of associative rings (general theory) (16Z05)

Related Items (7)

On Monomial Characters and Central Idempotents of Rational Group Algebras ⋮ Primitive idempotents of Schur rings. ⋮ Finite semisimple group algebra of a normally monomial group ⋮ Extremely strong Shoda pairs with \texttt{GAP}. ⋮ An algorithm to compute the Wedderburn decomposition of semisimple group algebras implemented in the GAP package \texttt{wedderga}. ⋮ The Group of Automorphisms of the Rational Group Algebra of a Finite Metacyclic Group ⋮ Computing the Wedderburn decomposition of group algebras by the Brauer–Witt theorem

Uses Software

• GAP
• wedderga

Cites Work

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• Generators of large subgroups of the unit group of integral group rings
• Calculating characters of \(p\)-groups
• On Monomial Characters and Central Idempotents of Rational Group Algebras
• Construction of Units in Integral Group Rings of Finite Nilpotent Groups
• Computing Irreducible Representations of Supersolvable Groups
• On the automorphism groups of rational group algebras of metacyclic groups
• CENTRAL IDEMPOTENTS IN THE RATIONAL GROUP ALGEBRA OF A FINITE NILPOTENT GROUP
• COMPUTING LARGE DIRECT PRODUCTS OF FREE GROUPS IN INTEGRAL GROUP RINGS
• A structure theorem for the unit group of the integral group ring of some finite groups
• The Schur subgroup of the Brauer group

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