The commutator algebra of a nilpotent matrix and an application to the theory of commutative Artinian algebras

DOI10.1016/j.jalgebra.2007.09.011zbMath1135.13010arXiv1206.6574OpenAlexW1978750326MaRDI QIDQ2474288

Tadahito Harima, Junzo Watanabe

Publication date: 5 March 2008

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

Full work available at URL: https://arxiv.org/abs/1206.6574

zbMATH Keywords

nilpotent matrixArtinian algebracommutator algebra

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Graded rings (13A02) Commutative Artinian rings and modules, finite-dimensional algebras (13E10)

Related Items

The central simple modules of Artinian Gorenstein algebras ⋮ Commuting nilpotent matrices and Artinian algebras. ⋮ The strong Lefschetz property for complete intersections defined by products of linear forms ⋮ Symmetric decomposition of the associated graded algebra of an Artinian Gorenstein algebra ⋮ Bound on the Jordan type of a generic nilpotent matrix commuting with a given matrix ⋮ The poset of the nilpotent commutator of a nilpotent matrix ⋮ The smallest part of the generic partition of the nilpotent commutator of a nilpotent matrix ⋮ Strata of vector spaces of forms in \({R = \mathsf k[x, y}\), and of rational curves in \({\mathbb{P}^k}\)] ⋮ Nilpotent matrices having a given Jordan type as maximum commuting nilpotent orbit ⋮ 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 ⋮ Artinian algebras and Jordan type

Cites Work

• The central simple modules of Artinian Gorenstein algebras
• On the irreducibility of commuting varieties of nilpotent matrices
• The weak and strong Lefschetz properties for Artinian \(K\)-algebras
• The strong Lefschetz property for Artinian algebras with non-standard grading
• The finite free extension of Artinian \(K\)-algebras with the strong Lefschetz property
• Associated graded algebra of a Gorenstein Artin algebra
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