dc.creator | Arenas, Manuel | |
dc.creator | Labra, Alicia | |
dc.date | 2017-03-23 | |
dc.date.accessioned | 2019-11-14T11:59:15Z | |
dc.date.available | 2019-11-14T11:59:15Z | |
dc.identifier | https://www.revistaproyecciones.cl/article/view/1298 | |
dc.identifier | 10.4067/S0716-09172014000100009 | |
dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/113089 | |
dc.description | It 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.format | application/pdf | |
dc.language | spa | |
dc.publisher | Universidad Católica del Norte. | es-ES |
dc.relation | https://www.revistaproyecciones.cl/article/view/1298/1010 | |
dc.rights | Derechos de autor 2014 Proyecciones. Journal of Mathematics | es-ES |
dc.source | Proyecciones. Journal of Mathematics; Vol 33 No 1 (2014); 123-132 | en-US |
dc.source | Proyecciones. Revista de Matemática; Vol. 33 Núm. 1 (2014); 123-132 | es-ES |
dc.source | 0717-6279 | |
dc.source | 0716-0917 | |
dc.subject | Locally nilpotent algebra | es-ES |
dc.subject | vector space | es-ES |
dc.subject | birrepresentation | es-ES |
dc.subject | álgebra localmente nilpotente | es-ES |
dc.subject | espacio vectorial | es-ES |
dc.subject | birrepresentación. | es-ES |
dc.title | Birrepresentations in a locally nilpotent variety | es-ES |
dc.type | info:eu-repo/semantics/article | |
dc.type | info:eu-repo/semantics/publishedVersion | |
dc.type | Artículo revisado por pares | es-ES |