Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598356 | Journal of Pure and Applied Algebra | 2007 | 17 Pages |
Abstract
Let AA be a standard graded Artinian KK-algebra, with char K=0K=0. We prove the following. 1.AA has the Weak Lefschetz Property (resp. Strong Lefschetz Property) if and only if Gr(z)(A) has the Weak Lefschetz Property (resp. Strong Lefschetz Property) for some linear form zz of AA.2.If AA is Gorenstein, then AA has the Strong Lefschetz Property if and only if there exists a linear form zz of AA such that all central simple modules of (A,z)(A,z) have the Strong Lefschetz Property. As an application of these theorems, we give some new classes of Artinian complete intersections with the Strong Lefschetz Property.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Tadahito Harima, Junzo Watanabe,