Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On homomorphisms from Ringel-Hall algebras to quantum cluster algebras   In \cite{rupel3},the authors defined algebra homomorphisms from the dual
Ringel-Hall algebra of certain hereditary abelian category $\mathcal{A}$ to an
appropriate $q$-polynomial algebra. In the case that $\mathcal{A}$ is the
representation category of an acyclic quiver, we give an alternative proof by
using the cluster multiplication formulas in \cite{DX}. Moreover, if the
underlying graph of $Q$ is bipartite and the matrix $B$ associated to the
quiver $Q$ is of full rank, we show that the image of the algebra homomorphisms
is in the corresponding quantum cluster algebra.

19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ