Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Auslander algebras and initial seeds for cluster algebras   Let $Q$ be a Dynkin quiver and $\Pi$ the corresponding set of positive roots.
For the preprojective algebra $\Lambda$ associated to $Q$ we produce a rigid
$\Lambda$-module $I_Q$ with $r=|\Pi|$ pairwise non-isomorphic indecomposable
direct summands by pushing the injective modules of the Auslander algebra of
$kQ$ to $\Lambda$.
  If $N$ is a maximal unipotent subgroup of a complex simply connected simple
Lie group of type $|Q|$, then the coordinate ring $C[N]$ is an upper cluster
algebra. We show that the elements of the dual semicanonical basis which
correspond to the indecomposable direct summands of $I_Q$ coincide with certain
generalized minors which form an initial cluster for $C[N]$, and that the
corresponding exchange matrix of this cluster can be read from the Gabriel
quiver of $End_{\Lambda}(I_Q)$.
  Finally, we exploit the fact that the categories of injective modules over
$\Lambda$ and over its covering $\tilde{\Lambda}$ are triangulated in order to
show several interesting identities in the respective stable module categories.

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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph