On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras

We describe of all finite dimensional uniserial representations of a commutative associative (resp. abelian Lie) algebra over a perfect (resp. sufficiently large perfect) field. In the Lie case the size of the field depends on the answer to following question, considered and solved in this paper. Le...

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Detalles Bibliográficos
Autores: Cagliero, Leandro Roberto, Szchetman, Fernando
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2014
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/32141
Acceso en línea:http://hdl.handle.net/11336/32141
Access Level:acceso abierto
Palabra clave:Uniserial Module
Lie Algebra
Associative Algebra
Primitive Element
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:We describe of all finite dimensional uniserial representations of a commutative associative (resp. abelian Lie) algebra over a perfect (resp. sufficiently large perfect) field. In the Lie case the size of the field depends on the answer to following question, considered and solved in this paper. Let $K/F$ be a finite separable field extension and let $x,yin K$. When is $F[x,y]=F[alpha x+eta y]$ for some non-zero elements $alpha,etain F$?