Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extended affine Lie algebras, vertex algebras and equivariant
  $\phi$-coordinated quasi modules   For any nullity $2$ extended affine Lie algebra $\mathcal{E}$ of maximal type
and $\ell\in\mathbb{C}$, we prove that there exist a vertex algebra
$V_{\mathcal{E}}(\ell)$ and an automorphism group $G$ of
$V_{\mathcal{E}}(\ell)$ equipped with a linear character $\chi$, such that the
category of restricted $\mathcal{E}$-modules of level $\ell$ is canonically
isomorphic to the category of $(G,\chi)$-equivariant $\phi$-coordinated quasi
$V_{\mathcal{E}}(\ell)$-modules. Moreover, when $\ell$ is a nonnegative
integer, there is a quotient vertex algebra $L_{\mathcal{E}}(\ell)$ of
$V_{\mathcal{E}}(\ell)$ modulo by a $G$-stable ideal, and we prove that the
integrable restricted $\mathcal{E}$-modules of level $\ell$ are exactly the
$(G,\chi)$-equivariant $\phi$-coordinated quasi
$L_{\mathcal{E}}(\ell)$-modules.

18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga