Representation Of Q-analog Virasoro-like Algebra

Let q∈C be a non-zero non-root of unity.In this thesis,we mainly consider the Z-graded modules of the intermediate seri(?)es over the q-analog Virasoro-like algebra L_q.In chapter 2,the classification of the Z-graded modules of the intermediate series over L_q has been solved,and some propersities of these modules are given; in chapter 3,we determine all the anti-linear anti-involutions over the Lie algebra L_q.Then with regarding to the Z-graded intermediate serial modules over L_q,we study the unitary of these modules and the corresponding Hermite form and the anti-linear anti-involutions.