The Representation Theory On Q-analog Virasoro-like Algebra

In this paper ,we will complete the classification of the Z-graded irreducible modules of the intermidiate series over the ra,nk two quantum torus L_q at roots of unity. In chapter 2 ,we recall the definition of rank two quantum torus L_q and some of its properties with q be a root of unity.In chapter 3 ,we construct six classes of the Z-graded modules of the intermidiate series for the derived Lie subalgebra L_q' of the quantum torus L_q. Then we study their reducibility and the isomorphisms between them .In chapter 4 ,we prove that a Z-graded L_q' -module of the intermidiate series must be isomorphic to one of the modules constructed in chapter 3.In chapter 5 ,we study the classification of the Z-graded modules over the C_q which is the center of L_q. In chapter 6 ,we complete the classification of the Z-graded irreducible modules of the intermidiate series over the rank two quantum torus L_q at roots of unity.