“…For standard graded Artinian Gorenstein K algebras A, the Strong Lefschetz property (SLP) means that there is l ∈ A 1 such that the multiplication maps µ l d−2k : A k → A d−k is an isomorphism for all k. The Weak Lefschetz property (WLP) means that there is l ∈ A 1 such that the multiplication maps µ l : A k → A k+1 have maximal rank for all k. In the algebraic context the Lefschetz properties is also a very important theme of research the last decades (see, for instance, [BI,BL,BMMNZ,MN1,MN2,St,St2,HMNW,MW,Go,GZ]).…”