Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantization of deformed cluster Poisson varieties   Fock and Goncharov described a quantization of cluster
$\mathcal{X}$-varieties (also known as cluster Poisson varieties) in [FG09].
Meanwhile, families of deformations of cluster $\mathcal{X}$-varieties were
introduced in [BFMNC18]. In this paper we show that the two constructions are
compatible -- we extend the Fock-Goncharov quantization of
$\mathcal{X}$-varieties to the families of [BFMNC18]. As a corollary, we obtain
that these families and each of their fibers have Poisson structures. We relate
this construction to the Berenstein-Zelevinsky quantization of
$\mathcal{A}$-varieties ([BZ05]). Finally, inspired by the counter-example to
quantum positivity of the quantum greedy basis in [LLRZ14], we compute a
counter-example to quantum positivity of the quantum theta basis.

16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
18
The categories of this paper are: econ