Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Companion bases for cluster-tilted algebras   Motivated by work of Barot, Geiss and Zelevinsky, we study a collection of
Z-bases (which we call companion bases) of the integral root lattice of a root
system of simply-laced Dynkin type. Each companion basis is associated with the
quiver of a cluster-tilted algebra of the corresponding type.
  In type A, we establish that the dimension vectors of the finitely generated
indecomposable modules over a cluster-tilted algebra may be obtained, up to
sign, by expanding the positive roots in terms of any companion basis for the
quiver of that algebra. This generalises part of Gabriel's Theorem.
  Also, we describe the relationship between different companion bases for the
same quiver and show how to mutate a companion basis for a quiver to produce a
companion basis for a mutation of that quiver.

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The categories of this paper are: stat
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The categories of this paper are: hep-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int