Related papers: Complexity of quiver mutation equivalence

We associate a quiver to a quasi-triangulation of a non-orientable marked surface and define a notion of quiver mutation that is compatible with quasi-cluster algebra mutation defined by Dupont and Palesi. Moreover, we use our quiver to…

Quiver mutation plays a crucial role in the definition of cluster algebras by Fomin and Zelevinsky. It induces an equivalence relation on the set of all quivers without loops and two-cycles. A quiver is called mutation-acyclic if it is…

We initiate the study of applications of machine learning to Seiberg duality, focusing on the case of quiver gauge theories, a problem also of interest in mathematics in the context of cluster algebras. Within the general theme of Seiberg…

The knots-quivers correspondence states that various characteristics of a knot are encoded in the corresponding quiver and the moduli space of its representations. However, this correspondence is not a bijection: more than one quiver may be…

Given two quivers, each with a reddening sequence, we show how to construct a plethora of mutation cycles. We give several examples, including a generalization of the construction of long mutation cycles in earlier work by the second…

We consider several computational problems related to conjugacy between subshifts of finite type, restricted to $k$-block codes: verifying a proposed $k$-block conjugacy, deciding if two shifts admit a $k$-block conjugacy, and reducing the…

The notion of mutation plays crucial roles in representation theory of algebras. Two kinds of mutation are well-known: tilting/silting mutation and quiver-mutation. In this paper, we focus on tilting mutation for symmetric algebras.…

The purpose of this article is to study the space of stability conditions $\stab(P_n)$ on the bounded derived category $\D^b(P_n)$ of finite dimensional representations of a quiver $P_n$ with two vertices and $n$ parallel arrows. There is a…

We show that the mutation class of a finite quiver without oriented cycles is finite if and only is the quiver is either Dynkin, extended Dynkin or has at most two vertices.

We consider the general notion of coloured quiver mutation and show that the mutation class of a coloured quiver $Q$, arising from an $m$-cluster tilting object associated with $H$, is finite if and only if $H$ is of finite or tame…

It is shown that certain transformations on quiver-dimension vector pairs induce isomorphisms on the corresponding moduli spaces of quiver representations and map a stable dimension vector to a stable dimension vector. This result combined…

We give an explicit description of the mutation classes of quivers of type \tilde{A}_n. Furthermore, we provide a complete classification of cluster tilted algebras of type \tilde{A}_n up to derived equivalence. We show that the bounded…

The set of forks is a class of quivers introduced by M. Warkentin, where every connected mutation-infinite quiver is mutation equivalent to infinitely many forks. Let $Q$ be a fork with $n$ vertices, and $\boldsymbol{w}$ be a…

We explore Seiberg-like dualities, or mutations, for ${\cal N}=4$ quiver quantum mechanics in the context of wall-crossing. In contrast to higher dimensions, the 1d Seiberg-duality must be performed with much care. With fixed…

We study the quiver with relations of the endomorphism algebra of an APR tilting module. We give an explicit description of the quiver with relations by graded quivers with potential (QPs) and mutations. The result also implies that…

We gave a classification of P and Q with a finite number of K-orbits of a double flag variety G/P*K/Q for a symmetric pair (G, K) when G=GL_{m+n} and K=GL_{m}*GL_{n}, and a description of K-orbits when the number of K-orbits of G/P*K/Q is…

In this note we prove NP-hardness of the following problem: Given a set of matrices, is there a convex combination of those that is a nonsingular M-matrix? Via known characterizations of M-matrices, our result establishes NP-hardness of…

In 2009, Keller and Yang categorified quiver mutation by interpreting it in terms of equivalences between derived categories. Their approach was based on Ginzburg's Calabi-Yau algebras and on Derksen-Weyman-Zelevinsky's mutation of quivers…

Let k a characteristic zero field. We give a characterization for the finite quiver k-algebras, based on double derivations. More precisely, we prove that if an associative and unitary k-algebra have a family of double derivations…

We give an effective characterisation of the walls in the variation of geometric invariant theory problem associated to a quiver and a dimension vector.