Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A geometric model for syzygies over 2-Calabi-Yau tilted algebras   In this article, we consider the class of 2-Calabi-Yau tilted algebras that
are defined by a quiver with potential whose dual graph is a tree. We call
these algebras \emph{dimer tree algebras} because they can also be realized as
quotients of dimer algebras on a disc. These algebras are wild in general. For
every such algebra $B$, we construct a polygon $\mathcal{S}$ with a
checkerboard pattern in its interior that gives rise to a category
$\text{Diag}(\mathcal{S})$. The indecomposable objects of
$\text{Diag}(\mathcal{S})$ are the 2-diagonals in $\mathcal{S}$, and its
morphisms are given by certain pivoting moves between the 2-diagonals. We
conjecture that the category $\text{Diag}(\mathcal{S})$ is equivalent to the
stable syzygy category over the algebra $B$, such that the rotation of the
polygon corresponds to the shift functor on the syzygies. In particular, the
number of indecomposable syzygies is finite and the projective resolutions are
periodic. We prove the conjecture in the special case where every chordless
cycle in the quiver is of length three.
  As a consequence, we obtain an explicit description of the projective
resolutions. Moreover, we show that the syzygy category is equivalent to the
2-cluster category of type $\mathbb{A}$, and we introduce a new derived
invariant for the algebra $B$ that can be read off easily from the quiver.

8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph