6533b827fe1ef96bd1285ae4
RESEARCH PRODUCT
On the graded identities and cocharacters of the algebra of 3×3 matrices
Daniela La Mattinasubject
Hilbert series and Hilbert polynomialNumerical AnalysisAlgebra and Number TheoryMatrixGraded ringSuperalgebraPolynomial identitySuperalgebraGraded Lie algebraFiltered algebraAlgebrasymbols.namesakeSettore MAT/02 - AlgebraDifferential graded algebrasymbolsAlgebra representationDiscrete Mathematics and CombinatoricsGeometry and TopologyAlgebraically closed fieldCocharaterMathematicsdescription
Abstract Let M2,1(F) be the algebra of 3×3 matrices over an algebraically closed field F of characteristic zero with non-trivial Z 2 -grading. We study the graded identities of this algebra through the representation theory of the hyperoctahedral group Z 2 ∼S n . After splitting the space of multilinear polynomial identities into the sum of irreducibles under the Z 2 ∼S n -action, we determine all the irreducible Z 2 ∼S n -characters appearing in this decomposition with non-zero multiplicity. We then apply this result in order to study the graded cocharacter of the Grassmann envelope of M2,1(F). Finally, using the representation theory of the general linear group, we determine all the graded polynomial identities of the algebra M2,1(F) up to degree 5.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2004-06-01 | Linear Algebra and its Applications |