2005/12/09 by Y. A. Bahturin, Yuri Bahturin, S. K. Sehgal +6 · 1 citation
Mathematics · Physics and Astronomy · #16W50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA) #math.RA #msc:16W50
paper · pdf · doi:10.48550/arxiv.math/0512202
arxiv created 2005/12/09 · openalex publication_date 2005/12/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a finite-dimensional algebra over an algebraically closed field F graded by an arbitrary group G. We prove that R is a graded division algebra if and only if it is isomorphic to a twisted group algebra of some finite subgroup of G. If the characteristic of F is zero or \rm char F does not divide the order of any finite subgroup of G then we prove that R is graded simple if and only if it is a matrix algebra over a finite-dimensional graded division algebra.