Centralizers in Lie Algebras

Centralizers in Lie Algebras

We determine the number of centralizers of different non-abelian finite dimensional Lie algebras over a specific field. Also, the concept of Lie algebras with abelian centralizers are studied and using a result of Bokut and Kukin [5], for a given residually free Lie algebra L , it is shown that L is...

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Veröffentlicht in:Indian journal of pure and applied mathematics 2018-03, Vol.49 (1), p.39-49
Hauptverfasser: Saffarnia, Somayeh, Moghaddam, Mohammad Reza R., Rostamyari, Mohammad Amin
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Applications of Mathematics
Lie groups
Mathematics
Mathematics and Statistics
Numerical Analysis
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Beschreibung
Zusammenfassung:We determine the number of centralizers of different non-abelian finite dimensional Lie algebras over a specific field. Also, the concept of Lie algebras with abelian centralizers are studied and using a result of Bokut and Kukin [5], for a given residually free Lie algebra L , it is shown that L is fully residually free if and only if every centralizer of non-zero elements of L is abelian.
ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-018-0252-0