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Universal central extension of direct limits of Hom-Lie algebras

  • Valiollah Khalili
Article
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Abstract

We prove that the universal central extension of a direct limit of perfect Hom- Lie algebras \((\mathcal{L_i,\;\alpha_{\mathcal{L}_i}})\) is (isomorphic to) the direct limit of universal central extensions of \((\mathcal{L_i,\;\alpha_{\mathcal{L}_i}})\). As an application we provide the universal central extensions of some multi-plicative Hom-Lie algebras. More precisely, we consider a family of multiplicative Hom-Lie algebras {(slk\((\mathcal{A})\), αk)}k∈I and describe the universal central extension of its direct limit.

Keywords

Hom-Lie algebra extension of Hom-Lie algebras and its direct limit 

MSC

17A30 17B55 17B60 17B99 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceArak UniversityArakIran

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