Corrigendum to “Classification of solvable Leibniz algebras with naturally graded filiform nilradical” [Linear Algebra Appl. 438 (7) (2013) 2973–3000]

There is a mistake in the description of complex solvable Leibniz algebras whose nilradical is a naturally graded filiform algebra [2, Theorem 4.3]. Namely, in the case where the dimension of the solvable Leibniz algebra with nilradical Fn1 is equal to n+2, it was asserted that there is no such alge...

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Bibliographic Details
Published in:Linear algebra and its applications 2016-10, Vol.507, p.513-517
Main Authors: Ladra, M., Masutova, K.K., Omirov, B.A.
Format: Article
Language:English
Subjects:
Derivation
Filiform algebra
Group of cohomology
Leibniz algebra
Natural graduation
Nilpotency
Nilradical
Rigidity
Solvability
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Summary:There is a mistake in the description of complex solvable Leibniz algebras whose nilradical is a naturally graded filiform algebra [2, Theorem 4.3]. Namely, in the case where the dimension of the solvable Leibniz algebra with nilradical Fn1 is equal to n+2, it was asserted that there is no such algebra. However, it was possible for us to find a unique (n+2)-dimensional solvable Leibniz algebra with nilradical Fn1. The corrected description is provided in this Corrigendum note. In addition, we establish the triviality of the second group of cohomology for this algebra with coefficients in itself, which implies its rigidity.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2016.07.012