Correction

Degenerations of Zinbiel and nilpotent Leibniz algebras (vol 66, 704, 2018)

Journal

LINEAR & MULTILINEAR ALGEBRA
Volume 70, Issue 5, Pages 993-995

Publisher

TAYLOR & FRANCIS LTD
DOI: 10.1080/03081087.2020.1749543

Keywords

Leibniz algebra; Zinbiel algebra; nilpotent algebra; degeneration

Categories

Funding

  1. Russian Science Foundation [119-71-10016]

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This paper points out that a 4-dimensional nilpotent Leibniz algebra was overlooked in previous classification studies, and provides the necessary corrections.
It was noted in Demir et al. [On classification of four-dimensional nilpotent Leibniz algebras. Comm Algebra. 2017;45(3):1012-1018]; Ismailov et al. [Degenerations of Leibniz and anticommutative algebras. Canad Math Bull. 2019;62(3):539-549] that there is a 4-dimensional nilpotent Leibniz algebra that is not included in the classification obtained in Albeverio et al. [Classification of 4-dimensional nilpotent complex Leibniz algebras. Extracta Math. 2006;21(3):197-210]. The construction of the graph of degenerations (see Kaygorodov et al. Degenerations of Zinbiel and nilpotent Leibniz algebras. Linear Multilinear Algebra. 2018;66(4):704-716) is based on the classification of Albeverio et al. [Classification of 4-dimensional nilpotent complex Leibniz algebras. Extracta Math. 2006;21(3):197-210] and for this reason, this graph does not contain the mentioned algebra. This omission and some other small inaccuracies are corrected in the present corrigendum.

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