Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cluster algebras of finite type via Coxeter elements and principal
  minors   We give a uniform geometric realization for the cluster algebra of an
arbitrary finite type with principal coefficients at an arbitrary acyclic seed.
This algebra is realized as the coordinate ring of a certain reduced double
Bruhat cell in the simply connected semisimple algebraic group of the same
Cartan-Killing type. In this realization, the cluster variables appear as
certain (generalized) principal minors.

10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
26
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: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph