Automorphisms, derivations, and central extensions of Lie algebras arising from quantum tori

Abstract

For a Lie algebra related to a quantum torus, we compute its automorphisms, derivations, and universal central extension. This Lie algebra is isomorphic to a subalgebra of the Lie algebra of derivations over the quantum torus, and moreover contains a subalgebra isomorphic to the centerless higher rank Virasoro algebra.