6533b7d5fe1ef96bd12652a9
RESEARCH PRODUCT
Gradings on the algebra of upper triangular matrices of size three
Alessio Cirritosubject
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 TheoryMathematicsdescription
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 ) .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-06-01 |