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Keller–Reiten's main theorem in Acyclic Calabi–Yau categories implies that if $\mathcal{C}$ is a $2$-Calabi–Yau (algebraic) triangulated category admitting a cluster-tilting object $T$ such that the ...

Let $P$ be an $n$-element poset and $J(P)$ the distributive lattice of its order ideals (i.e., the downwards-closed sets). For each $I\in J(P)$ let $x_I \in \mathbb{R}^{n}$ be the indicator function ...

Setup: Let $B$ be a skew-symmetrisable integer matrix and $\mathcal{A}$ be the cluster algebra with principal coefficients at a seed with mutation matrix $\tilde{B}$ whose principal part is equal to $...

Let $ \mathcal A$ be the complex cluster algebra obtained from the initial seed $(a,x, B)$ where : $x$ stands for a $n$-tuple $(x_1,\ldots,x_n)$ of complex indeterminates, idem for $a=(a_1,\ldots,...

I am reading this paper strongly primitiv species with potentials I : mutations. In page 6, they give the definition of weighted quiver: a weighted quiver is a pair $(Q,d)$, where $Q$ is a loop-...