Geodesic
Universal central extension of direct limits of Hom-Lie algebras
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 275-293 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
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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     title = {Universal central extension of direct limits of {Hom-Lie} algebras},
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     pages = {275--293},
     year = {2019},
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Khalili, Valiollah. Universal central extension of direct limits of Hom-Lie algebras. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 275-293. doi: 10.21136/CMJ.2018.0290-17

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