Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classifying {\tau}-tilting modules over preprojective algebras of Dynkin
  type   We study support $\tau$-tilting modules over preprojective algebras of Dynkin
type. We classify basic support $\tau$-tilting modules by giving a bijection
with elements in the corresponding Weyl groups. Moreover we show that they are
in bijection with the set of torsion classes, the set of torsion-free classes
and other important objects in representation theory. We also study
$g$-matrices of support $\tau$-tilting modules, which show terms of minimal
projective presentations of indecomposable direct summands. We give an explicit
description of $g$-matrices and prove that cones given by $g$-matrices coincide
with chambers of the associated root systems.

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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-ph