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Corrigendum to: “Degenerations of Zinbiel and nilpotent Leibniz algebras”. (English) Zbl 1482.17061

Summary: It was noted in [I. Demir et al., Commun. Algebra 45, No. 3, 1012–1018 (2017; Zbl 1418.17007); N. Ismailov et al., Can. Math. Bull. 62, No. 3, 539–549 (2019; Zbl 1477.17020)] that there is a 4-dimensional nilpotent Leibniz algebra that is not included in the classification obtained in [S. Albeverio et al., Extr. Math. 21, No. 3, 197–210 (2006; Zbl 1137.17002)]. The construction of the graph of degenerations (see [the authors, Linear Multilinear Algebra 66, No. 4, 704–716 (2018; Zbl 1472.17100)]) is based on the classification of Albeverio et al. [loc. cit.] 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.

MSC:

17D99 Other nonassociative rings and algebras
17A30 Nonassociative algebras satisfying other identities
17A32 Leibniz algebras
Full Text: DOI

References:

[1] Kaygorodov, I.; Popov, Yu; Pozhidaev, A., Degenerations of Zinbiel and nilpotent Leibniz algebras, Linear Multilinear Algebra, 66, 4, 704-716 (2018) · Zbl 1472.17100 · doi:10.1080/03081087.2017.1319457
[2] Albeverio, S.; Omirov, B.; Rakhimov, I., Classification of 4-dimensional nilpotent complex Leibniz algebras, Extracta Math, 21, 3, 197-210 (2006) · Zbl 1137.17002
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