Search results for " G-graded algebras"

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Gradings on the algebra of upper triangular matrices of size three

2013

Abstract Let UT 3 ( F ) be the algebra of 3 × 3 upper triangular matrices over a field F . On UT 3 ( F ) , up to isomorphism, there are at most five non-trivial elementary gradings and we study the graded polynomial identities for such gradings. In case F is of characteristic zero we give a complete description of the space of multilinear graded identities in the language of Young diagrams through the representation theory of a Young subgroup of S n . We finally compute the multiplicities in the graded cocharacter sequence for every elementary G -grading on UT 3 ( F ) .

Numerical AnalysisMultilinear mapPolynomialAlgebra and Number TheoryMathematics::Commutative AlgebraMathematics::Rings and AlgebrasZero (complex analysis)Triangular matrixField (mathematics)Representation theorypolynomial identity G-graded algebras cocharacters graded ideals of identitiesCombinatoricsAlgebraSettore MAT/02 - AlgebraDifferential graded algebraDiscrete Mathematics and CombinatoricsGeometry and TopologyIsomorphismComputer Science::Information TheoryMathematics
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