Derivations and lower cohomology of Lie algebra crossed modules
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University of Niš, Faculty of Sciences and Mathematics
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Abstract
In 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.
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Ladra, M., Pérez-Rodríguez, A. (2026). Derivations and lower cohomology of Lie algebra crossed modules. Filomat, 40(9), 3213-3224
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Research partially supported by the Agencia Estatal de Investigación (Spain), grants PID2020-115155GB-I00 and PID2024155502NB-I00 from MICIU/AEI/10.13039/501100011033 and from FEDER, UE, and by the Xunta de Galicia through the Competitive Reference Groups(GRC),ED431C2023/31. The second author was also supported by the FPU21/05685 scholarship from the Ministerio de Educación y Formación Profesional (Spain).