dc.contributor.author | Garcia Martinez, Xabier | |
dc.contributor.author | Tsishyn, M. | |
dc.contributor.author | Van der Linden, T. | |
dc.contributor.author | Vienne, C. | |
dc.date.accessioned | 2021-11-18T09:11:52Z | |
dc.date.available | 2021-11-18T09:11:52Z | |
dc.date.issued | 2021-06-24 | |
dc.identifier.citation | Proceedings of the Edinburgh Mathematical Society, 64(3): 555-573 (2021) | spa |
dc.identifier.issn | 00130915 | |
dc.identifier.issn | 14643839 | |
dc.identifier.uri | http://hdl.handle.net/11093/2701 | |
dc.description | Financiado para publicación en acceso aberto: Universidade de Vigo/CISUG | |
dc.description.abstract | Just 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.sponsorship | Ministerio de Economía y Competitividad | Ref. MTM2016-79661-P | spa |
dc.language.iso | eng | en |
dc.publisher | Proceedings of the Edinburgh Mathematical Society | spa |
dc.rights | Attribution 4.0 International | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.title | Algebras with representable representations | en |
dc.type | article | spa |
dc.rights.accessRights | openAccess | spa |
dc.identifier.doi | 10.1017/S0013091521000304 | |
dc.identifier.editor | https://www.cambridge.org/core/product/identifier/S0013091521000304/type/journal_article | spa |
dc.publisher.departamento | Matemáticas | spa |
dc.publisher.grupoinvestigacion | Matemáticas | spa |
dc.subject.unesco | 12 Matemáticas | spa |
dc.subject.unesco | 1201 Álgebra | spa |
dc.date.updated | 2021-11-18T09:00:34Z | |
dc.computerCitation | pub_title=Proceedings of the Edinburgh Mathematical Society|volume=64|journal_number=3|start_pag=555|end_pag=573 | spa |
dc.references | The 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-P | spa |