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