Structures Of A Class Of Lie Algebra Related To Virasoro Algebra

In this present paper, we study a class of Lie algebra related to Virasoro algebra. Through the graded algebra, we derive its derivative algebra, and prove that all the derivations are inner derivations. Further more, we prove that the Lie algebra is complete. We also obtain its second cohomology group by means of some delicate techniques and some deep observation. Accordingly, we determine its universal central extension. Finally, we calculate and get its bialgebra structure through a convenient method using some Known cohomology group of some related algebra.