On the maximal nilpotent orbit that intersects the centralizer of a matrix

DOI10.1007/s00031-022-09704-0zbMath1493.15062OpenAlexW4214844526MaRDI QIDQ2120884

Roberta Basili

Publication date: 1 April 2022

Published in: Transformation Groups (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00031-022-09704-0

zbMATH Keywords

commuting matricesnilpotent orbitsmaximal orbit

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Commutativity of matrices (15A27) Canonical forms, reductions, classification (15A21) Combinatorial aspects of commutative algebra (05E40)

Related Items (1)

Artinian algebras and Jordan type

Cites Work

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• Pairs of commuting nilpotent matrices, and Hilbert function
• On pairs of commuting nilpotent matrices
• On the irreducibility of commuting varieties of nilpotent matrices
• On the irreducibility of varieties of commuting matrices
• 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
• Two results on centralisers of nilpotent elements
• On the nilpotent commutator of a nilpotent matrix
• The upper bound for the index of nilpotency for a matrix commuting with a given nilpotent matrix
• Singularities in the Nilpotent Scheme of a Classical Group
• The variety of pairs of commuting nilpotent matrices is irreducible

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