Derivations and lower cohomology of Lie algebra crossed modules

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dc.contributor.affiliationUniversidade de Santiago de Compostela. Departamento de Matemáticas
dc.contributor.affiliationUniversidade de Santiago de Compostela. Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga)
dc.contributor.authorLadra González, Manuel
dc.contributor.authorPérez Rodríguez, Andrés
dc.date.accessioned2026-05-08T07:39:15Z
dc.date.available2026-05-08T07:39:15Z
dc.date.issued2026-04-15
dc.description.abstractIn 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.
dc.description.sponsorshipResearch 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).
dc.identifier.citationLadra, M., Pérez-Rodríguez, A. (2026). Derivations and lower cohomology of Lie algebra crossed modules. Filomat, 40(9), 3213-3224
dc.identifier.essn2406-0933
dc.identifier.urihttps://hdl.handle.net/10347/47179
dc.journal.titleFilomat
dc.language.isoeng
dc.publisherUniversity of Niš, Faculty of Sciences and Mathematics
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-115155GB-I00/ES/HOMOLOGIA, HOMOTOPIA E INVARIANTES CATEGORICOS EN GRUPOS Y ALGEBRAS NO ASOCIATIVAS
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2024-2027/PID2024-155502NB/ES/HOMOLOGIA, HOMOTOPIA E INVARIANTES CATEGORICOS EN GRUPOS Y ALGEBRAS NO ASOCIATIVAS
dc.relation.publisherversionhttps://www.pmf.ni.ac.rs/filomat-content/2026/40-9/FILOMAT%2040-9.html
dc.rights.accessRightsopen access
dc.subjectLie algebra crossed modules
dc.subjectDerivations
dc.subjectUniversal enveloping
dc.subjectCohomology
dc.titleDerivations and lower cohomology of Lie algebra crossed modules
dc.typejournal article
dc.type.hasVersionVoR
dspace.entity.typePublication
relation.isAuthorOfPublication2b7d6a14-fd3c-41da-a849-ff485bf2c3bc
relation.isAuthorOfPublication.latestForDiscovery2b7d6a14-fd3c-41da-a849-ff485bf2c3bc

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