Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensor product decompositions of II$_1$ factors arising from extensions
  of amalgamated free product groups   In this paper we introduce a new family of icc groups $\Gamma$ which satisfy
the following product rigidity phenomenon, discovered in [DHI16] (see also
[dSP17]): all tensor product decompositions of the II$_1$ factor $L(\Gamma)$
arise only from the canonical direct product decompositions of the underlying
group $\Gamma$. Our groups are assembled from certain HNN-extensions and
amalgamated free products and include many remarkable groups studied throughout
mathematics such as graph product groups, poly-amalgam groups, Burger-Mozes
groups, Higman group, various integral two-dimensional Cremona groups, etc. As
a consequence, we obtain several new examples of groups that give rise to prime
factors.

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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: funct-an