LAUSR

In this paper, we investigate the Lie algebra structures of weight one subspaces of C2-cofinite vertex operator superalgebras. We also show that for any positive integer k, vertex operator superalgebras Lsl(1|n+1)(k, 0) and Losp(2|2n)(k, 0) have infinitely many irreducible admissible modules. As a consequence, we give a proof of the fact that Lg(k, 0) is C2-cofinite if and only if g is either a simple Lie algebra, or g = osp(1|2n), and k is a nonnegative integer. As an application, we show that LG(3)(1, 0) is a vertex operator superalgebra such that the category of LG(3)(1, 0)modules is semisimple but LG(3)(1, 0) is not C2-cofinite.