Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Indecomposable Non-Simple $\mathbb{N}$-graded Vertex Algebras   In this paper, we study an impact of Leibniz algebras on the algebraic
structure of $\mathbb{N}$-graded vertex algebras. We provide easy ways to
characterize indecomposable non-simple $\mathbb{N}$-graded vertex algebras
$\oplus_{n=0}^{\infty}V_{(n)}$ such that $\dim V_{(0)}\geq 2$. Also, we examine
the algebraic structure of $\mathbb{N}$-graded vertex algebras
$V=\oplus_{n=0}^{\infty}V_{(n)}$ such that $\dim~V_{(0)}\geq 2$ and $V_{(1)}$
is a (semi)simple Leibniz algebra that has $sl_2$ as its Levi factor. We show
that under suitable conditions this type of vertex algebra is indecomposable
but not simple. Along the way we classify vertex algebroids associated with
(semi)simple Leibniz algebras that have $sl_2$ as their Levi factor.

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The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
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The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
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The categories of this paper are: acc-phys