The strong Lefschetz property for Artinian algebras with non-standard grading

Abstract: Let be a graded Artinian K-algebra, where and . (The grading may not necessarily be standard.) Then A has the strong Lefschetz property if there exists an element such that the multiplication is bijective for every . The main results obtained in this paper are as follows: [1.] A has the strong Lefschetz property if and only if there is a linear form such that has the strong Lefschetz property. [2.] If A is Gorenstein, then A has the strong Lefschetz property if and only if there is a linear form such that all central simple modules of have the strong Lefschetz property. [3.] A finite free extension of an Artinian K-algebra with the strong Lefschetz property has the strong Lefschetz property if the fiber does. [4.] The complete intersection defined by power sums of consecutive degrees has the strong Lefschetz property. [Copyright &y& Elsevier]