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Twisted Modules for Vertex Operator Superalgebras and Associative Algebras
 Author(s): Petersen, Charles Anthony
 Advisor(s): Dong, Chongying
 et al.
Abstract
Let $V$ be a vertex operator superalgebra and $\sigma$ the order $2$ automorphism \linebreak associated with the superstructure of $V$. For a finite order automorphism $g$ with $o(g\sigma)=T'$, we follow~\cite{DONGLIMASONAGNV} to construct a sequence of associative algebras $\AGNV$ for $n\in \frac{1}{T'}\Z_+$ such that $A_{g,n\frac{1}{T'}}(V)$ is a quotient of $\AGNV$. There is a bijection between the irreducible $\AGNV$modules which cannot factor through $A_{g,n\frac{1}{T'}}(V)$ and the irreducible admissible $g$twisted $V$modules. These results are then\newline applied to $g$rational vertex operator superalgebras. In this case it is shown that $V$ is $g$rational if and only if all the $\AGNV$ are finitedimensional. Taking $n=0$ we obtain the associative algebra $\AGV$ constructed in~\cite{DONGZHAOAGV}. With $g=1$ we recover $A_n(V)$ as in~\cite{JIANGJIANG}.
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