Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: C-vectors via $\tau$-tilting theory   Inspired by the tropical duality in cluster algebras, we introduce c-vectors
for finite-dimensional algebras via $\tau$-tilting theory. Let $A$ be a
finite-dimensional algebra over a field $k$. Each c-vector of $A$ can be
realized as the (negative) dimension vector of certain indecomposable
$A$-module and hence we establish the sign-coherence property of this kind of
$c$-vectors. We then study the positive c-vectors for certain classes of
finite-dimensional algebras. More precisely, we establish the equalities
between the set of positive c-vectors and the set of dimension vectors of
exceptional modules for quasitilted algebras and representation-directed
algebras respectively. This generalizes the equalitites of c-vectors for
acyclic cluster algebras obtained by Ch\'{a}vez. To this end, a short proof for
the sign-coherence of c-vectors for skew-symmetric cluster algebras has been
given in the appendix.

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The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
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The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin