Kurdiani, Revaz Lie triple systems and Leibniz algebras. (English) Zbl 1477.17026 Georgian Math. J. 28, No. 1, 109-116 (2021). Summary: The present paper deals with the Lie triple systems via Leibniz algebras. A perfect Lie algebra as a perfect Leibniz algebra and as a perfect Lie triple system is considered and the appropriate universal central extensions are studied. Using properties of Leibniz algebras, it is shown that the Lie triple system universal central extension is either the universal central extension of the Leibniz algebra or the universal central extension of the Lie algebra. MSC: 17A32 Leibniz algebras 17A40 Ternary compositions 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.) Keywords:Leibniz algebras; Lie algebras; Lie triple systems; universal central extensions PDFBibTeX XMLCite \textit{R. Kurdiani}, Georgian Math. J. 28, No. 1, 109--116 (2021; Zbl 1477.17026) Full Text: DOI References: [1] N. Jacobson, Lie and Jordan triple systems, Amer. J. Math. 71 (1949), 149-170. · Zbl 0034.16903 [2] W. G. Lister, A structure theory of Lie triple systems, Trans. Amer. Math. Soc. 72 (1952), 217-242. · Zbl 0046.03404 [3] O. Loos, Symmetric Spaces. I, II, W. A. Benjamin, New York, 1969. · Zbl 0175.48601 [4] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Pure Appl. Math. 80, Academic Press, New York, 1978. · Zbl 0451.53038 [5] J.-L. Loday, A noncommutative version of Lie algebras: the Leibniz algebras (in French), Enseign. Math. (2) 39 (1993), no. 3-4, 269-293. · Zbl 0806.55009 [6] J.-L. Loday, Cyclic Homology, Grundlehren Math. Wiss. 301, Springer, Berlin, 1992. · Zbl 0780.18009 [7] J.-L. Loday and T. Pirashvili, Universal enveloping algebras of Leibniz algebras and (co)homology, Math. Ann. 296 (1993), no. 1, 139-158. · Zbl 0821.17022 [8] R. Kurdiani and T. Pirashvili, A Leibniz algebra structure on the second tensor power, J. Lie Theory 12 (2002), no. 2, 583-596. · Zbl 1062.17002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.