Centralizers in Lie Algebras |
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| Authors: | Somayeh Saffarnia Mohammad Reza R Moghaddam Mohammad Amin Rostamyari |
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| Institution: | 1.International Campus, Faculty of Mathematical Sciences,Ferdowsi University of Mashhad,Mashhad,Iran;2.Department of Mathematics,Khayyam University,Mashhad,Iran;3.Department of Pure Mathematics, Centre of Excellence in Analysis on Algebraic Structures (CEAAS),Ferdowsi University of Mashhad,Mashhad,Iran |
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| Abstract: | 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. |
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