Twisted associative algebras associated to vertex algebras

Let $V$ be a vertex algebra and $g$ an automorphism of $V$ of order $T$. We construct a sequence of associative algebras ${\tilde{A}}_{g,n}(V)$ for any $n\in (1\mathrm{/}T)\mathbb{N}$, which are not depend on the conformal structure of $V$. We show that for a vertex operator algebra, $g$-rationality, $g$-regularity, and twisted fusion rules are independent of the choice of the conformal vector.