Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A cohomology theory of grading-restricted vertex algebras   We introduce a cohomology theory of grading-restricted vertex algebras. To
construct the {\it correct} cohomologies, we consider linear maps from tensor
powers of a grading-restricted vertex algebra to "rational functions valued in
the algebraic completion of a module for the algebra," instead of linear maps
from tensor powers of the algebra to a module for the algebra. One subtle
complication arising from such functions is that we have to carefully address
the issue of convergence when we compose these linear maps with vertex
operators. In particular, for each $n\in \mathbb{N}$, we have an inverse system
$\{H^{n}_{m}(V, W)\}_{m\in \mathbb{Z}_{+}}$ of $n$-th cohomologies and an
additional $n$-th cohomology $H_{\infty}^{n}(V, W)$ of a grading-restricted
vertex algebra $V$ with coefficients in a $V$-module $W$ such that
$H_{\infty}^{n}(V, W)$ is isomorphic to the inverse limit of the inverse system
$\{H^{n}_{m}(V, W)\}_{m\in \mathbb{Z}_{+}}$. In the case of $n=2$, there is an
additional second cohomology denoted by $H^{2}_{\frac{1}{2}}(V, W)$ which will
be shown in a sequel to the present paper to correspond to what we call
square-zero extensions of $V$ and to first order deformations of $V$ when
$W=V$.

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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin