This work demonstrates isomorphism in finite-dimensional trivial central extensions of 3-dimensional Lie algebras, suggesting new insights into Lie superalgebras.
Constructing Lie superalgebras from Lie algebras is an important subject for studying Lie superalgebras. In this paper, all the superizations are presented for finite-dimensional trivial central extensions of a class of 3-dimensional complex or real Lie algebras. In particular, up to isomorphism, superizations are determined for 1-dimensional trivial central extensions of these Lie algebras by considering orbits of an action of [Formula: see text] on [Formula: see text], where [Formula: see text] consists of [Formula: see text]-invariant symmetric bilinear mappings and [Formula: see text].
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Zhao et al. (2025) studied this question.
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