Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal two-parameter even spin $\mathcal{W}_{\infty}$-algebra   We construct the unique two-parameter vertex algebra which is freely
generated of type ${\mathcal W}(2,4,6,\dots)$, and generated by the weights $2$
and $4$ fields. Subject to some mild constraints, all vertex algebras of type
${\mathcal W}(2,4,\dots, 2N)$ for some $N$, can be obtained as quotients of
this universal algebra. This includes the $B$ and $C$ type principal ${\mathcal
W}$-algebras, the $\mathbb{Z}_2$-orbifolds of the $D$ type principal ${\mathcal
W}$-algebras, and many others which arise as cosets of affine vertex algebras
inside larger structures. As an application, we classify all coincidences among
the simple quotients of the $B$ and $C$ type principal ${\mathcal W}$-algebras,
as well as the $\mathbb{Z}_2$-orbifolds of the $D$ type principal ${\mathcal
W}$-algebras. Finally, we use our classification to give new examples of
principal ${\mathcal W}$-algebras of $B$, $C$, and $D$ types, which are lisse
and rational.

14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
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The categories of this paper are: stat
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio