Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flatness of Tensor Products and Semi-Rigidity for $C_2$-cofinite Vertex
  Operator Algebras II   Let V be a simple C_2-cofinite VOA of CFT-type and we assume that there is a
simple module U such that \Hom_V(U\boxtimes V',V)\not=0 where V' is a
restricted dual of V. As the author has shown, an S-transformation S(\Psi_V) of
a trace function \Psi_V on V corresponding \begin{pmatrix}0&-1\cr
1&0\end{pmatrix} may contain pseudo-trace functions. Our assumption in this
paper is that no pseudo-trace functions appear in S(\Psi_V). Under these
assumptions, we prove that every V-module W is semirigid and \Psi_W appears in
S(\Psi_V). As a corollary of our main theorem, a fixed point subVOA of a
rational VOA of CFT-type by an automorphism of finite order becomes rational if
fixed point subVOA is C_2-cofinite.

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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: econ
1
The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an