The superalgebra of W (2,2) and its modules of the intermediate series.

In this paper, we study a new Lie superalgebra constructed by a 2|2-dimensional Balinsky–Novikov superalgebra, which is called the superalgebra ofW(2,2). It can be realized from semi product of theW-algebraW(2,2) and its module of the intermediate series. Finally, we determine all modules of the intermediate series over this superalgebra. Since it is difficult to do so directly, we make it by using modules of the intermediate series over the trivial super extension of the Witt algebra. [ABSTRACT FROM PUBLISHER]