Illinois Journal of Mathematics

Lefschetz elements of Artinian Gorenstein algebras and Hessians of homogeneous polynomials

Toshiaki Maeno and Junzo Watanabe

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We give a characterization of the Lefschetz elements in Artinian Gorenstein rings over a field of characteristic zero in terms of the higher Hessians. As an application, we give new examples of Artinian Gorenstein rings which do not have the strong Lefschetz property.

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Illinois J. Math., Volume 53, Number 2 (2009), 591-603.

First available in Project Euclid: 23 February 2010

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Zentralblatt MATH identifier

Primary: 13E10: Artinian rings and modules, finite-dimensional algebras
Secondary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]


Maeno, Toshiaki; Watanabe, Junzo. Lefschetz elements of Artinian Gorenstein algebras and Hessians of homogeneous polynomials. Illinois J. Math. 53 (2009), no. 2, 591--603. doi:10.1215/ijm/1266934795.

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