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Isoclinic extensions of Lie superalgebras

Abstract We study the notion of isoclinism on central extensions of Lie superalgebras and discuss some conditions under which central extensions are isoclinic as well as some results on isoclinic homomorphisms of central extensions. We also define the notion of factor sets on central extensions and investigate their relation with stem extensions of Lie superalgebras. Moreover, it is shown under certain conditions that the notion of isoclinism is equivalent to isomorphism.