Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rationality of the vertex algebra $V_L^+$ when $L$ is a nondegenerate
  even lattice of arbitrary rank   In this paper we prove that the vertex algebra $V_L^+$ is rational if $L$ is
a negative definite even lattice of finite rank, or if $L$ is a non-degenerate
even lattice of a finite rank that is neither positive definite nor negative
definite. In particular, for such even lattices $L$, we show that the Zhu
algebras of the vertex algebras $V_L^+$ are semisimple. This extends the result
of Abe which establishes the rationality of $V_L^+$ when $L$ is a positive
definite even lattice of finite rank.

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The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom