The Grunewald–O'Halloran Conjecture for Nilpotent Lie Algebras of Rank ≥1

Joan Felipe Herrera-Granada; Paulo Tirao

doi:10.1080/00927872.2015.1044097

The Grunewald–O'Halloran Conjecture for Nilpotent Lie Algebras of Rank ≥1

Joan Felipe Herrera-Granada, Paulo Tirao^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Grunewald and O'Halloran conjectured in 1993 that every complex nilpotent Lie algebra is the degeneration of another, nonisomorphic, Lie algebra. We prove the conjecture for the class of nilpotent Lie algebras admitting a semisimple derivation, and also for 7-dimensional nilpotent Lie algebras. The conjecture remains open for characteristically nilpotent Lie algebras of dimension grater than or equal to 8.

Original language	English
Pages (from-to)	2180-2192
Number of pages	13
Journal	Communications in Algebra
Volume	44
Issue number	5
DOIs	https://doi.org/10.1080/00927872.2015.1044097
State	Published - 3 May 2016
Externally published	Yes

Keywords

Deformations
Degenerations
Grunewald-O'Halloran conjecture
Nilpotent Lie algebras
Vergne's conjecture

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10.1080/00927872.2015.1044097

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abstract = "Grunewald and O'Halloran conjectured in 1993 that every complex nilpotent Lie algebra is the degeneration of another, nonisomorphic, Lie algebra. We prove the conjecture for the class of nilpotent Lie algebras admitting a semisimple derivation, and also for 7-dimensional nilpotent Lie algebras. The conjecture remains open for characteristically nilpotent Lie algebras of dimension grater than or equal to 8.",

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Y1 - 2016/5/3

N2 - Grunewald and O'Halloran conjectured in 1993 that every complex nilpotent Lie algebra is the degeneration of another, nonisomorphic, Lie algebra. We prove the conjecture for the class of nilpotent Lie algebras admitting a semisimple derivation, and also for 7-dimensional nilpotent Lie algebras. The conjecture remains open for characteristically nilpotent Lie algebras of dimension grater than or equal to 8.

AB - Grunewald and O'Halloran conjectured in 1993 that every complex nilpotent Lie algebra is the degeneration of another, nonisomorphic, Lie algebra. We prove the conjecture for the class of nilpotent Lie algebras admitting a semisimple derivation, and also for 7-dimensional nilpotent Lie algebras. The conjecture remains open for characteristically nilpotent Lie algebras of dimension grater than or equal to 8.

KW - Deformations

KW - Degenerations

KW - Grunewald-O'Halloran conjecture

KW - Nilpotent Lie algebras

KW - Vergne's conjecture

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The Grunewald–O'Halloran Conjecture for Nilpotent Lie Algebras of Rank ≥1

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Keywords

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