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math.RA2025
An Algorithm for Determining Lie Algebra Types
Tu N. T. C. Nguyen, Tuan A. Nguyen, Vu A. Le
This paper investigates the Jordan--Kronecker invariant of finite dimensional complex Lie algebras. We present an explicit algorithm for determining the type of a given Lie algebra…
math.RA2025
Complete and cocomplete Lie algebras with injective- and projective-type properties
Vu A. Le, Hoa Q. Duong, Tuan A. Nguyen
In the category of modules, injective and projective objects are characterized by the splitting of short exact sequences. Motivated by this principle, we investigate analogous phen…
math.RA2025
Complete and cocomplete Lie algebras with injective and projective properties
Vu A. Le, Hoa Q. Duong, Tuan A. Nguyen
Motivated by the classical correspondence between short exact sequences and splitting properties in module theory, this paper examines the projective and injective analogues within…