Ladra González, ManuelPérez Rodríguez, Andrés2026-05-082026-05-082026-04-15Ladra, M., Pérez-Rodríguez, A. (2026). Derivations and lower cohomology of Lie algebra crossed modules. Filomat, 40(9), 3213-3224https://hdl.handle.net/10347/47179In this paper, we define the derivation of a Lie algebra crossed module and prove that it can be represented by the augmentation ideal of a crossed module. Additionally, we introduce the first cohomology groups for n = 0,1, of a crossed module with coefficients, and we establish their connection to the classical Chevalley-Eilenberg Lie algebra cohomology.engLie algebra crossed modulesDerivationsUniversal envelopingCohomologyjournal article2406-0933open access