Czechoslovak Mathematical Journal, Vol. 69, No. 1, pp. 275-293, 2019


Universal central extension of direct limits of Hom-Lie algebras

Valiollah Khalili

Received June 14, 2017.   Published online November 19, 2018.

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 multiplicative Hom-Lie algebras. More precisely, we consider a family of multiplicative Hom-Lie algebras $\{({\rm sl}_k(a), \alpha_k)\}_{k\in I}$ and describe the universal central extension of its direct limit.
Keywords:  Hom-Lie algebra; extension of Hom-Lie algebras and its direct limit
Classification MSC:  17A30, 17B55, 17B60, 17B99
DOI:  10.21136/CMJ.2018.0290-17


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Affiliations:   Valiollah Khalili, Department of Mathematics, Faculty of Science, Arak University, 386156-8-8349, Iran, e-mail: V-Khalili@araku.ac.ir


 
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