Czechoslovak Mathematical Journal, first online, pp. 1-44
Generalized semidirect sums of Lie algebras and their modules
Rui Lu, Youjun Tan
Received September 22, 2024. Published online January 25, 2025.
Abstract: Generalized semidirect sums of Lie algebras and their modules are introduced, which are not necessarily (non)-Abelian extensions and may be applied to construct Lie algebras from modules. Some properties of generalized semidirect sums are described. In particular, it is shown that finite dimensional non-solvable Lie algebras can be realized as generalized semidirect sums. The complete classification up to isomorphism of all generalized semidirect sums of $\mathfrak{sl}_2$ and its finite-dimensional irreducible modules is given.
Keywords: Lie algebra; module; generalized semidirect sum
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Affiliations: Rui Lu, College of Mathematics, Chengdu Normal University, No.99 East Haike Road, Chengdu 611130, P. R.China, e-mail: 061064@cdnu.edu.cn; Youjun Tan (corresponding author), College of Mathematics, Sichuan University, Chengdu 610064, P. R. China, e-mail: ytan@scu.edu.cn
