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SOME PROPERTIES ON ISOCLINISM OF LIE ALGEBRAS AND COVERS

ALI REZA SALEMKAR

Faculty of Mathematical Sciences, Shahid Beheshti University, G.C., Tehran, Iran

Corresponding author.

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HADI BIGDELY

Faculty of Mathematical Sciences, Shahid Beheshti University, G.C., Tehran, Iran

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, and

VAHID ALAMIAN

Department of Mathematics, Azad University of Mashhad, Iran

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https://doi.org/10.1142/S0219498808002965Cited by:15 (Source: Crossref)

Abstract

In this paper, we give some equivalent conditions for Lie algebras to be isoclinic. In particular, it is shown that if two Lie algebras L and K are isoclinic then L can be constructed from K and vice versa using the operations of forming direct sums, taking subalgebras, and factoring Lie algebras. We also study connection between isoclinic and the Schur multiplier of Lie algebras. In addition, we deal with some properties of covers of Lie algebras whose Schur multipliers are finite dimensional and prove that all covers of any abelian Lie algebra have Hopfian property. Finally, we indicate that if a Lie algebra L belongs to some certain classes of Lie algebras then so does its cover.

This research was supported by a grant from Iran National Science Foundation (INSF).

Keywords:

AMSC: 17B40, 17B99

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