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Universal central extension of direct limits of Hom-Lie algebras

Valiollah Khalili (2019)

Czechoslovak Mathematical Journal

We prove that the universal central extension of a direct limit of perfect Hom-Lie algebras ( ℒ i , α ℒ i ) is (isomorphic to) the direct limit of universal central extensions of ( ℒ i , α ℒ i ) . As an application we provide the universal central extensions of some multiplicative Hom-Lie algebras. More precisely, we consider a family of multiplicative Hom-Lie algebras { ( sl k ( å ) , α k ) } k ∈ I and describe the universal central extension of its direct limit.

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