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 |
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2021
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| Acceso en línea: | http://hdl.handle.net/11086/20530 https://doi.org/10.4153/CMB-2013-046-9 |
| Aporte de: |
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I10-R141-11086-20530 |
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dspace |
| institution |
Universidad Nacional de Córdoba |
| institution_str |
I-10 |
| repository_str |
R-141 |
| collection |
Repositorio Digital Universitario (UNC) |
| language |
Inglés |
| topic |
Uniserial module Lie algebra Associative algebra Primitive element |
| spellingShingle |
Uniserial module Lie algebra Associative algebra Primitive element Cagliero, Leandro Roberto Szechtman, Fernando On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras |
| topic_facet |
Uniserial module Lie algebra Associative algebra Primitive element |
| description |
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? |
| format |
article |
| author |
Cagliero, Leandro Roberto Szechtman, Fernando |
| author_facet |
Cagliero, Leandro Roberto Szechtman, Fernando |
| author_sort |
Cagliero, Leandro Roberto |
| title |
On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras |
| title_short |
On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras |
| title_full |
On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras |
| title_fullStr |
On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras |
| title_full_unstemmed |
On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras |
| title_sort |
on the theorem of the primitive element with applications to the representation theory of associative and lie algebras |
| publishDate |
2021 |
| url |
http://hdl.handle.net/11086/20530 https://doi.org/10.4153/CMB-2013-046-9 |
| work_keys_str_mv |
AT caglieroleandroroberto onthetheoremoftheprimitiveelementwithapplicationstotherepresentationtheoryofassociativeandliealgebras AT szechtmanfernando onthetheoremoftheprimitiveelementwithapplicationstotherepresentationtheoryofassociativeandliealgebras |
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Repositorios |
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