Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A reflection equivalence for Gorenstein-projective quiver
  representations   For $\Lambda$ a selfinjective algebra, and $Q$ a finite quiver without
oriented cycles, the algebra $\Lambda Q$ is a Gorenstein algebra and the
category ${\rm Gproj}\Lambda Q$ of Gorenstein-projective $\Lambda Q$-modules is
a Frobenius category. For a sink $v$ of $Q$, we define a functor $F(v) :
\underline{\rm Gproj}\Lambda Q\to \underline{\rm Gproj}\Lambda Q(v)$ between
the stable categories modulo projectives, where $Q(v)$ is obtained from $Q$ by
changing the direction of each arrow ending in $v$. The functor is given by an
explicit construction on the level of objects and homomorphisms. Our main
result states that $F(v)$ is an equivalence of categories. In the case where
the underlying graph of $Q$ is a tree, we deduce that the stable category
$\underline{\rm Gproj}\Lambda Q$ does not depend on the orientation of $Q$.
Moreover, if $Q$ is a quiver of type $\mathbb A_3$ and $\Lambda=k[T]/(T^n)$ the
bounded polynomial algebra, we use the symmetry of the octahedron in the
octahedral axiom to verify that the composition of twelve reflections yields
the identity on objects.

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The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th