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dc.contributor.authorGarcia Martinez, Xabier 
dc.contributor.authorTsishyn, M.
dc.contributor.authorVan der Linden, T.
dc.contributor.authorVienne, C.
dc.date.accessioned2021-11-18T09:11:52Z
dc.date.available2021-11-18T09:11:52Z
dc.date.issued2021-06-24
dc.identifier.citationProceedings of the Edinburgh Mathematical Society, 64(3): 555-573 (2021)spa
dc.identifier.issn00130915
dc.identifier.issn14643839
dc.identifier.urihttp://hdl.handle.net/11093/2701
dc.descriptionFinanciado para publicación en acceso aberto: Universidade de Vigo/CISUG
dc.description.abstractJust like group actions are represented by group automorphisms, Lie algebra actions are represented by derivations: up to isomorphism, a split extension of a Lie algebra B by a Lie algebra X corresponds to a Lie algebra morphism B→Der(X) from B to the Lie algebra Der(X) of derivations on X . In this article, we study the question whether the concept of a derivation can be extended to other types of non-associative algebras over a field K , in such a way that these generalized derivations characterize the K -algebra actions. We prove that the answer is no, as soon as the field K is infinite. In fact, we prove a stronger result: already the representability of all abelian actions – which are usually called representations or Beck modules – suffices for this to be true. Thus, we characterize the variety of Lie algebras over an infinite field of characteristic different from 2 as the only variety of non-associative algebras which is a non-abelian category with representable representations. This emphasizes the unique role played by the Lie algebra of linear endomorphisms gl(V) as a representing object for the representations on a vector space V .en
dc.description.sponsorshipMinisterio de Economía y Competitividad | Ref. MTM2016-79661-Pspa
dc.language.isoengen
dc.publisherProceedings of the Edinburgh Mathematical Societyspa
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.titleAlgebras with representable representationsen
dc.typearticlespa
dc.rights.accessRightsopenAccessspa
dc.identifier.doi10.1017/S0013091521000304
dc.identifier.editorhttps://www.cambridge.org/core/product/identifier/S0013091521000304/type/journal_articlespa
dc.publisher.departamentoMatemáticasspa
dc.publisher.grupoinvestigacionMatemáticasspa
dc.subject.unesco12 Matemáticasspa
dc.subject.unesco1201 Álgebraspa
dc.date.updated2021-11-18T09:00:34Z
dc.referencesThe first author is a Postdoctoral Fellow of the Research Foundation–Flanders (FWO) and was supported by Ministerio de Economía y Competitividad (Spain), with grant number MTM2016-79661-Pspa


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    Attribution 4.0 International
    Except where otherwise noted, this item's license is described as Attribution 4.0 International