On 3-dimensional complex Hom-Lie algebras (vol 555, pg 361, 2020)

JOURNAL OF ALGEBRA

卷:562

Correction

Garcia-Delgado, R.²  Salgado, G.¹  Sanchez-Valenzuela, O. A.² 

[1] Zona Univ, UASLP, Fac Ciencias, Av Salvador Nava S-N, San Luis Potosi 78290, Slp, Mexico

[2] Ctr Invest Matemat AC, Unidad Merida, Yuc, Mexico

关键词: Hom-Lie algebras;    Skew-symmetric bilinear maps;    Classification;    Automorphism groups;    Canonical forms;   

DOI  :  10.1016/j.jalgebra.2020.07.002

来源: Elsevier

【 摘 要 】

We wish to fix an error in [1]. The list of representatives of the isomorphism classes of skew-symmetric products mu : g x g -> gfor a complex 3-dimensional vector space g given there in Proposition 3.5 corresponding to the rank-2 degenerate products characterized by (2) in Proposition 3.3, were collapsed into a single representative, whereas a one-parameter family of representatives should have been obtained, as it is well known from the classification of 3-dimensional Lie algebras. The mistake affects the statements of Propositions 3.5 and 5.4. This note gives the correct statements of these two results. The rest is unaffected. (C) 2020 Elsevier Inc. All rights reserved.

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