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Oleksandra Gasanova: On Lefschetz properties of graded artinian algebras

Time: Mon 2020-11-30 15.00 - 16.00

Location: Zoom, meeting ID: 657 3341 0804

Participating: Oleksandra Gasanova, Uppsala


Let \(R=K[x_1, ... , x_n]\), where \(\mathrm{char}(K)=0\). A graded artinian \(K\)-algebra \(A:=R/J\) is said to have the Strong Lefschetz Property (SLP) if there exists a linear form \(L\) such that for any degree \(d\) and for any power \(k\), multiplication by \(L^k\) has maximal rank as a linear map from \(A_d\) to \(A_{d+k}\), where \(A_d\) denotes the \(d\)th graded component of \(A\). In this case \(L\) is called an SL-element of \(A\). An algebra as above is said to have SLP in the narrow sense if additionally the h-vector of \(A\) is symmetric.
In my talk I will discuss a technique which in some cases helps us establish the SLP. I will also introduce a class of monomial ideals which has the SLP in the narrow sense and will generalise several results on this topic.