Some properties of c-covers of a pair of Lie algebras |
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Authors: | Homayoon Arabyani |
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Institution: | Department of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran. E-Mail arabyani.h@gmail.com, h.arabyani@iau-neyshabur.ac.ir |
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Abstract: | In H. Safa and H. Arabyani, On c-nilpotent multiplier and c-covers of a pair of Lie algebras, Commun. Algebra 45(10) (2017), 4429–4434], we characterized the structure of the c-nilpotent multiplier of a pair of Lie algebras in terms of its c-covering pairs and discussed some results on the existence of c-covers of a pair of Lie algebras. In the present paper, it is shown under some conditions that a relative c-central extension of a pair of Lie algebras is a homomorphic image of a c-covering pair. Moreover, we prove that a c-cover of a pair of finite dimensional Lie algebras, under some assumptions, has a unique domain up to isomorphism and also that every perfect pair of Lie algebras admits at least one c-cover. Finally, we discuss a result concerning the isoclinism of c-covering pairs. |
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Keywords: | Primary 17B30 17B60 Secondary 17B99 |
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