The strong Lefschetz property of the coinvariant ring of the Coxeter group of type \(H_{4}\)

DOI10.1016/j.jalgebra.2007.06.016zbMath1134.13003arXivmath/0703003OpenAlexW2024402152MaRDI QIDQ2470385

Akihito Wachi, Yasuhide Numata

Publication date: 14 February 2008

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703003

zbMATH Keywords

strong Lefschetz propertycoinvariant rings

Mathematics Subject Classification ID

Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Actions of groups on commutative rings; invariant theory (13A50)

Related Items (10)

Lefschetz properties and hyperplane arrangements ⋮ Lefschetz properties for higher order Nagata idealizations ⋮ Strong Lefschetz elements of the coinvariant rings of finite Coxeter groups ⋮ Waring problems and the Lefschetz properties ⋮ The Lefschetz elements of coinvariant algebras of binary polyhedral groups. ⋮ Equivariant coinvariant rings, Bott-Samelson rings and Watanabe's bold conjecture ⋮ The Hodge theory of Soergel bimodules. ⋮ Lefschetz elements of Artinian Gorenstein algebras and hessians of homogeneous polynomials ⋮ The strong Lefschetz property for coinvariant rings of finite reflection groups ⋮ The Jordan type of graded Artinian Gorenstein algebras

Uses Software

• Macaulay2

Cites Work

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• Strong Lefschetz elements of the coinvariant rings of finite Coxeter groups
• The Dilworth number of Artin Gorenstein rings
• Schubert calculus of a Coxeter group
• The weak and strong Lefschetz properties for Artinian \(K\)-algebras
• The finite free extension of Artinian \(K\)-algebras with the strong Lefschetz property
• Erratum to: ``The finite free extension of Artinian \(K\)-algebras with the strong Lefschetz property
• Basic sets of invariant polynomials for finite reflection groups
• Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property
• Associated graded algebra of a Gorenstein Artin algebra
• The Lefschetz Property for Componentwise Linear Ideals and Gotzmann Ideals

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