Search results for "Brauer group"

showing 2 items of 2 documents

Complex group algebras of finite groups: Brauer’s Problem 1

2005

Brauer’s Problem 1 asks the following: what are the possible complex group algebras of finite groups? It seems that with the present knowledge of representation theory it is not possible to settle this question. The goal of this paper is to announce a partial solution to this problem. We conjecture that if the complex group algebra of a finite group does not have more than a fixed number m m of isomorphic summands, then its dimension is bounded in terms of m m . We prove that this is true for every finite group if it is true for the symmetric groups.

Computer Science::Machine LearningModular representation theoryPure mathematicsFinite groupBrauer's theorem on induced charactersGroup (mathematics)General MathematicsMathematicsofComputing_GENERALComputer Science::Digital LibrariesRepresentation theoryCombinatoricsStatistics::Machine LearningGroup of Lie typeSymmetric groupComputer Science::Mathematical SoftwareComputer Science::Programming LanguagesBrauer groupMathematicsElectronic Research Announcements of the American Mathematical Society
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Brauer characters and coprime action

2016

Abstract It is an open problem to show that under a coprime action, the number of invariant Brauer characters of a finite group is the number of the Brauer characters of the fixed point subgroup. We prove that this is true if the non-abelian simple groups satisfy a stronger condition.

Discrete mathematicsModular representation theoryPure mathematicsFinite groupAlgebra and Number TheoryBrauer's theorem on induced charactersCoprime integers010102 general mathematics02 engineering and technologyFixed point021001 nanoscience & nanotechnology01 natural sciencesSimple group0101 mathematicsInvariant (mathematics)Mathematics::Representation Theory0210 nano-technologyBrauer groupMathematicsJournal of Algebra
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