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On rigid 3-dimensional Hom-Lie algebras. (English) Zbl 1500.17020

The paper under review explores and determines all the rigid 3-dimensional multiplicative Hom-Lie algebras over the field of complex numbers. A key to reach the goal is to study deformations of multiplicative Hom-Lie algebras whose product is also a Lie bracket. A byproduct of the paper is to recover the well-known classification of 3-dimensional multiplicative (non-Lie) Hom-Lie algebras.

MSC:

17B61 Hom-Lie and related algebras
17B56 Cohomology of Lie (super)algebras
17D30 (non-Lie) Hom algebras and topics
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