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dc.creatorArenas, Manuel
dc.creatorLabra, Alicia
dc.date2017-03-23
dc.date.accessioned2019-11-14T11:59:15Z
dc.date.available2019-11-14T11:59:15Z
dc.identifierhttps://www.revistaproyecciones.cl/article/view/1298
dc.identifier10.4067/S0716-09172014000100009
dc.identifier.urihttps://revistaschilenas.uchile.cl/handle/2250/113089
dc.descriptionIt is known that commutative algebras satisfying the identity of degree four ((yx)x)x + γ((xx)x) = 0, with γ in the field and γ ≠ —1 are locally nilpotent. In this paper we study the birrepresentations of an algebra A that belongs to a variety ν of locally nilpotent algebras. We prove that if the split null extension of a birrepresentation of an algebra A ∈ ν by a vector space M is locally nilpotent, then it is trivial or reducible. As corollaries we get that if A is finitely generated, then every birrepresentation is trivial or reducible and that every finite-dimensional birrepresentation is equivalent to a birrepre-sentation consisting of strictly upper triangular matrices. We also prove that the multiplicative universal envelope of a finitely generated algebra in V is nilpotent, therefore it is finite-dimensional.es-ES
dc.formatapplication/pdf
dc.languagespa
dc.publisherUniversidad Católica del Norte.es-ES
dc.relationhttps://www.revistaproyecciones.cl/article/view/1298/1010
dc.rightsDerechos de autor 2014 Proyecciones. Journal of Mathematicses-ES
dc.sourceProyecciones. Journal of Mathematics; Vol 33 No 1 (2014); 123-132en-US
dc.sourceProyecciones. Revista de Matemática; Vol. 33 Núm. 1 (2014); 123-132es-ES
dc.source0717-6279
dc.source0716-0917
dc.subjectLocally nilpotent algebraes-ES
dc.subjectvector spacees-ES
dc.subjectbirrepresentationes-ES
dc.subjectálgebra localmente nilpotentees-ES
dc.subjectespacio vectoriales-ES
dc.subjectbirrepresentación.es-ES
dc.titleBirrepresentations in a locally nilpotent varietyes-ES
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.typeArtículo revisado por pareses-ES


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