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

We describe 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...

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Autores principales: Cagliero, Leandro Roberto, Szechtman, Fernando
Formato: article
Lenguaje:Inglés
Publicado: 2021
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Acceso en línea:http://hdl.handle.net/11086/20530
https://doi.org/10.4153/CMB-2013-046-9
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Sumario:We describe 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, y ∈ K. When is F[x, y] = F[αx + βy] for some nonzero elements α, β ∈ F?