Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simplicity of a vertex operator algebra whose Griess algebra is the
  Jordan algebra of symmetric matrices   Let $r \in \BC$ be a complex number, and $d \in \BZ_{\ge 2}$ a positive
integer greater than or equal to 2. Ashihara and Miyamoto introduced a vertex
operator algebra $\Vam$ of central charge $dr$, whose Griess algebra is
isomorphic to the simple Jordan algebra of symmetric matrices of size $d$. In
this paper, we prove that the vertex operator algebra $\Vam$ is simple if and
only if $r$ is not an integer.
  Further, in the case that $r$ is an integer (i.e., $\Vam$ is not simple), we
give a generator system of the maximal proper ideal $I_{r}$ of the VOA $\Vam$
explicitly.

31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
24
The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
12
The categories of this paper are: nucl-th