Wedderburn decomposition of finite group algebras.

DOI10.1016/j.ffa.2005.08.002zbMath1111.20005OpenAlexW2030104872MaRDI QIDQ865382

Osnel Broche, Ángel Del Río

Publication date: 14 February 2007

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2005.08.002

zbMATH Keywords

finite fieldscoding theoryWedderburn decompositionsprimitive central idempotentssemisimple group algebras

Mathematics Subject Classification ID

Group rings (16S34) Group rings of finite groups and their modules (group-theoretic aspects) (20C05)

Related Items (21)

On equivalent classes of minimal abelian codes ⋮ On the embedding of finite solvable groups ⋮ On idempotents and the number of simple components of semisimple group algebras ⋮ Group algebras and coding theory ⋮ Semisimple metacyclic group algebras. ⋮ Codes from dihedral 2-groups ⋮ Finite group algebras of nilpotent groups: a complete set of orthogonal primitive idempotents. ⋮ The twisted group ring isomorphism problem over fields ⋮ Primitive idempotents of Schur rings. ⋮ Finite semisimple group algebra of a normally monomial group ⋮ Structure of finite dihedral group algebra. ⋮ Semisimple finite group algebra of a generalized strongly monomial group ⋮ Unnamed Item ⋮ On \(\ast\)-clean group rings over finite fields ⋮ Unnamed Item ⋮ An algorithm to compute the Wedderburn decomposition of semisimple group algebras implemented in the GAP package \texttt{wedderga}. ⋮ Minimum distance and idempotent generators of minimal cyclic codes of length ${p_1}^{\alpha_1}{p_2}^{\alpha_2}{p_3}^{\alpha_3}$ ⋮ Left dihedral codes over finite chain rings ⋮ Computing the Wedderburn decomposition of group algebras by the Brauer–Witt theorem ⋮ The Algebraic Structure of Finite Metabelian Group Algebras ⋮ Construction of minimal non-abelian left group codes

Cites Work

• Metacyclic error-correcting codes
• Reed‐muller codes: an ideal theory approach
• On Monomial Characters and Central Idempotents of Rational Group Algebras
• CENTRAL IDEMPOTENTS IN THE RATIONAL GROUP ALGEBRA OF A FINITE NILPOTENT GROUP
• On the theory of group codes
• The Schur subgroup of the Brauer group
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