Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graded quantum cluster algebras and an application to quantum
  Grassmannians   We introduce a framework for $\mathbb{Z}$-gradings on cluster algebras (and
their quantum analogues) that are compatible with mutation. To do this, one
chooses the degrees of the (quantum) cluster variables in an initial seed
subject to a compatibility with the initial exchange matrix, and then one
extends this to all cluster variables by mutation. The resulting grading has
the property that every (quantum) cluster variable is homogeneous.
  In the quantum setting, we use this grading framework to give a construction
that behaves somewhat like twisting, in that it produces a new quantum cluster
algebra with the same cluster combinatorics but with different
quasi-commutation relations between the cluster variables.
  We apply these results to show that the quantum Grassmannians admit quantum
cluster algebra structures, as quantizations of the cluster algebra structures
on the classical Grassmannian coordinate ring found by Scott. This is done by
lifting the quantum cluster algebra structure on quantum matrices due to
Gei{\ss}, Leclerc and Schr\"{o}er and completes earlier work of the authors on
the finite-type cases.

3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th