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

Abstract

For a Lie algebra $\mathfrak{g}$ related to a quantum torus, we compute its automorphisms, derivations, and universal central extension. This Lie algebra $\mathfrak{g}$ 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.

Keywords:

• Automorphism
• central extension
• derivation
• higher rank Virasoro algebra
• quantum torus

MATHEMATICAL SUBJECT CLASSIFICATION:

• 17B05
• 17B40
• 17B56
• 17B68

Additional information

Funding

The author is supported by the National Natural Science Foundation of China (no. 11626157) and the Science and Technology Foundation of Education Department of Jiangxi Province (no. GJJ161044).