Representations of some quantum tori Lie subalgebras.

In this paper, we define the q-analog Virasoro-like Lie subalgebras in x∞ = a∞(b∞, c∞, d∞). The embedding formulas into x∞ are introduced. Irreducible highest weight representations of Aq, Bq, and Cq-series of the q-analog Virasoro-like Lie algebras in terms of vertex operators are constructed. We also construct the polynomial representations of the Aq, Bq, Cq, and Dq-series of the q-analog Virasoro-like Lie algebras. [ABSTRACT FROM AUTHOR]