The central simple modules of Artinian Gorenstein algebras |
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Authors: | Tadahito Harima Junzo Watanabe |
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Affiliation: | a Department of Mathematics, Hokkaido University of Education, Kushiro 085-8580, Japan b Department of Mathematics, Tokai University, Hiratsuka 259-1292, Japan |
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Abstract: | Let A be a standard graded Artinian K-algebra, with char K=0. We prove the following. - 1.
- A has the Weak Lefschetz Property (resp. Strong Lefschetz Property) if and only if has the Weak Lefschetz Property (resp. Strong Lefschetz Property) for some linear form z of A.
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- If A is Gorenstein, then A has the Strong Lefschetz Property if and only if there exists a linear form z of A such that all central simple modules of (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. |
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Keywords: | 13A99 13H10 |
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