On Rationality of Vertex Operator Superalgebras

In this paper, we prove that g-rationality of a vertex operator superalgebra
$V=V_{\bar 0}\oplus V_{\bar 1}$
for all g∈G implies the rationality of V
^G
, and also implies that each irreducible V
^G
-module is a submodule of an irreducible g-twisted V -module for some g∈G, where G is any finite abelian subgroup of Aut(V). We also prove that, for any finite solvable G, rationality of V
^G
implies the g-rationality of V for any g∈G.