The Structure And Representation Of A New Class Of Block Algebras

Block algebra is a kind of infinite dimensional Lie algebras, and it was first in-troduced by R. Block in 1958. Recently, it has gained great interest of the domestic and foreign mathematicians, and at the same time it has achieved rapid develop-ment. Based on this, the research on a new type of Block algebra has become an important topic, and has important role in it.In this paper, we systematically research the structure and representations of a new type of Block algebra. Firstly, we study the construction of a new type of Block algebra, and we prove that it is Lie algebras. Secondly, we study the unique nontrivial central extension and second cohomology in the aspect of structure. Last but not least, we research the classification of irreducible quasifinite modules, and furthermore we describe the highest weight module in terms of the generated series in the aspect of representations.