A Contraction Lie Algebra Of Quantum Torus And Its Derivations And Universal Central Extension

In this paper, using the contraction technique, we construct a new infinite dimensionalLie algebra from rank two quantum tori. In the first part, we study the strcture of the new Liealgebra, we prove that it can be seen as a Abelion extension of Virasoro-like algebra. In thesecond part, we prove this Lie algebra is finitely generated, then we study its derivations andwe determine all of its derivations. Finally, we calculate2-cocycle on this Lie algebra, fromwhich we obtain its universal central extension.