Universal central extension of direct limits of Hom-Lie algebras

Khalili, Valiollah

Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 275-293

Abstract (VO)

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 $\{({\rm sl}_{k}(å), \alpha _k)\}_{k\in I}$ and describe the universal central extension of its direct limit.

Détail

DOI : 10.21136/CMJ.2018.0290-17

Classification : 17A30, 17B55, 17B60, 17B99
Keywords: Hom-Lie algebra; extension of Hom-Lie algebras and its direct limit

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