Associative superalgebras for Z-graded vertex operator superalgebra

Abstract

For a vertex superalgebra V, we construct a sequence of associative superalgebras $\widetilde{A_n}\left(V\right)$ for nonnegative integer n, which are not depend on the conformal structure of V. Based on this, we show that the rationality, regularity and fusion rules are independent of the choice of the conformal vector for $Z$-graded vertex operator superalgebra.