Semisimple Group (and Loop) Algebras over Finite Fields

2009/07/09 by Raul Antônio Ferraz, Raul A. Ferraz, Ferraz, Raul A. +5
Engineering · Mathematics · #20C05 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #graph theory and CDMA systems #math.RT #msc:20C05

paper · pdf · doi:10.48550/arxiv.0907.1592

openalex publication_date 2009/07/09 · arxiv created 2010/09/03 · arxiv updated 2010/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the structure of the semisimple group algebra of certain groups over the rationals and over those finite fields where the Wedderburn decompositions have the least number of simple components. We apply our work to obtain similar information about the loop algebras of indecomposable RA loops and to produce negative answers to the isomorphism problem over various fields.

Citations

• Idempotents in group algebras and minimal abelian codes

Related

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• On idempotents and the number of simple components of semisimple group algebra
• The algebraic structure of finite metabelian group algebras
• An elementary approach to Wedderburn's structure theory
• On the Wedderburn decomposition of the total ring of quotients of certain Iwasawa algebras