Search results for "Frobenius–Schur indicator"

showing 2 items of 2 documents

Characters, bilinear forms and solvable groups

2016

Abstract We prove a number of results about the ordinary and Brauer characters of finite solvable groups in characteristic 2, by defining and using the concept of the extended nucleus of a real irreducible character. In particular we show that the Isaacs canonical lift of a real irreducible Brauer character has Frobenius–Schur indicator +1. We also show that the principal indecomposable module corresponding to a real irreducible Brauer character affords a quadratic geometry if and only if each extended nucleus is a split extension of a nucleus.

Algebra and Number TheoryBrauer's theorem on induced charactersMathematics::Rings and Algebras010102 general mathematicsBilinear form01 natural sciencesCombinatoricsLift (mathematics)Frobenius–Schur indicatorQuadratic equationSolvable group0103 physical sciences010307 mathematical physics0101 mathematicsMathematics::Representation TheoryIndecomposable moduleMathematicsJournal of Algebra
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An infinite family of counterexamples to a conjecture on positivity

2021

Recently, G. Mason has produced a counterexample of order 128 to a conjecture in conformal field theory and tensor category theory in [Ma]. Here we easily produce an infinite family of counterexamples, the smallest of which has order 72.

Frobenius–Schur indicatorPure mathematicsAlgebra and Number TheoryConjectureConformal field theoryTensor (intrinsic definition)Order (group theory)Geometry and TopologyCategory theoryMathematical PhysicsAnalysisMathematicsCounterexampleRendiconti del Seminario Matematico della Università di Padova
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