161 research outputs found
The strong Lefschetz property for Artinian algebras with non-standard grading
We define the strong Lefschetz property for finite graded modules over graded
Artinian algebras whose grading is not necessarily standard. We show that most
results which have been obtained for Artinian algebras with standard grading
can be extended for non-standard grading. Our results on the strong Lefschetz
property for non-standard grading can be used to prove that certain Artinian
complete intersections with standard grading have the strong Lefschetz
property.Comment: 24 pages, To appear in Journal of Algebr
Vandermonde determinantal ideals
We show that the ideal generated by maximal minors (i.e., -minors) of
a Vandermonde matrix is radical and Cohen-Macaulay. Note that
this ideal is generated by all Specht polynomials with shape .Comment: 6 pages, simplified the proof of the main result. To appear in Math.
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Determinants of incidence and Hessian matrices arising from the vector space lattice
Let be the lattice of subspaces
of the -dimensional vector space over the finite field and
let be the graded Gorenstein algebra defined over
which has as a basis. Let be the Macaulay dual
generator for . We compute explicitly the Hessian determinant
evaluated at the point and relate it to the determinant of the incidence
matrix between and . Our exploration is
motivated by the fact that both of these matrices arise naturally in the study
of the Sperner property of the lattice and the Lefschetz property for the
graded Artinian Gorenstein algebra associated to it
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