# Oleksandra Gasanova: On Lefschetz properties of graded artinian algebras

Time: Mon 2020-11-30 15.00 - 16.00

Lecturer: Oleksandra Gasanova, Uppsala

Location:

### Abstract

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.

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