Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of Noncommuting Quadrilaterals of Factors   A quadrilateral of factors is an irreducible inclusion of factors $N \subset
M$ with intermediate subfactors $P$ and $Q$ such that $P$ and $Q$ generate $M$
and the intersection of $P$ and $Q$ is $N$. We investigate the structure of a
non-commuting quadrilateral of factors with all the elementary inclusions
$P\subset M$, $Q\subset M$, $N\subset P$, and $N\subset Q$ 2-supertransitive.
In particular we classify such quadrilaterals with the indices of the
elementary subfactors less than or equal to 4. We also compute the angles
between $P$ and $Q$ for quadrilaterals coming from $\alpha$-induction and
asymptotic inclusions.

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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: physics