Deformed higher rank Heisenberg-Virasoro algebras

In this paper, we study a class of infinitesimal deformations of the centerless higher rank Heisenberg–Virasoro algebras. Explicitly, the universal central extensions, derivations and isomorphism classes of these algebras are determined.

Lie triple systems and Leibniz algebras

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.