In this chapter, we survey Elias and Williamson's proof of Soergel's conjecture on the
characters of Soergel bimodules. Their work actually establishes a “Hodge theory” for …

Abstract Let A= ⨁ _ i= 0^ c A_ i, A c≠ 0, be a graded Artinian algebra. We say that A has the
weak Lefschetz property (WLP) if there exists an element L∈ A 1 such that the multiplication …

Lefschetz elements of Artinian Gorenstein algebras and Hessians of homogeneous polynomials
Page 1 Illinois Journal of Mathematics Volume 53, Number 2, Summer 2009, Pages 591–603 S …

We study the generic Jordan type of standard graded Artinian Gorenstein algebras, it is a
finer invariant than whether the algebra satisfies some of the Lefschetz properties. We prove …

For the coinvariant rings of finite Coxeter groups of types other than H 4, we show that a
homogeneous element of degree one is a strong Lefschetz element if and only if it is not …

We prove the Lefschetz property for a certain class of finite-dimensional Gorenstein algebras
associated to matroids. Our result implies the Sperner property of the vector space lattice …

In this paper we prove that a deformed tensor product of two Lefschetz algebras is a
Lefschetz algebra. We then use this result in conjunction with some basic Schubert calculus …

In this article, we study the weak and strong Lefschetz properties, and the related notion of
almost revlex ideal, in the non-Artinian case, proving that several results known in the …

We study a generalization of Nagata idealization for level algebras. These algebras are
standard graded Artinian algebras whose Macaulay dual generator is given explicitly as a …

Let $ A $ be a standard graded $\mathbb {K} $-algebra of finite type over an algebraically
closed field of characteristic zero. We use apolarity to construct, for each degree $ k $, a …