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: | , |
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| Formato: | article |
| Lenguaje: | Inglés |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | http://hdl.handle.net/11086/20530 https://doi.org/10.4153/CMB-2013-046-9 |
| Aporte de: |
| 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? |
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