6533b853fe1ef96bd12acb0b
RESEARCH PRODUCT
The graded identities of upper triangular matrices of size two
A. Valentisubject
Filtered algebraCombinatoricsPolynomialAlgebra and Number TheoryMathematics::Commutative AlgebraDifferential graded algebraGraded ringTriangular matrixHyperoctahedral groupRepresentation theoryMathematicsGraded Lie algebradescription
AbstractLet UT2 be the algebra of 2×2 upper triangular matrices over a field F. We first classify all possible gradings on UT2 by a group G. It turns out that, up to isomorphism, there is only one non-trivial grading and we study all the graded polynomial identities for such algebra. 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 the hyperoctahedral group. We finally establish a result concerning the rate of growth of the identities for such algebra by proving that its sequence of graded codimensions has almost polynomial growth.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2002-07-01 | Journal of Pure and Applied Algebra |