Non-additive Lie centralizer of strictly upper triangular matrices
| Autor: | Driss Aiat Hadj Ahmed |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Extracta Mathematicae, Vol 34, Iss 1 (2019) |
| Druh dokumentu: | article |
| ISSN: | 0213-8743 2605-5686 |
| Popis: | Let F be a field of zero characteristic, let Nn (F ) denote the algebra of n × n strictly upper triangular matrices with entries in F , and let f : Nn (F ) → Nn (F ) be a non-additive Lie centralizer of Nn (F ) , that is, a map satisfying that f ([X, Y ]) = [f (X), Y ] for all X, Y ∈ Nn (F ) . We prove that f (X) = λX + η (X) where λ ∈ F and η is a map from Nn (F ) into its center Z (Nn (F ) ) satisfying that η([X, Y ]) = 0 for every X, Y in Nn (F ) . |
| Databáze: | Directory of Open Access Journals |
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