Harish-Chandra modules for the q-analog Virasoro-like algebra

Let be the q-analog Virasoro-like algebra. In this paper we prove that any Harish-Chandra module of with nontrivial center is isomorphic to a generalized highest weight module. Moreover, we show that a generalized highest weight Harish-Chandra module of is induced from an irreducible module of a Heisenberg subalgebra of .