Related papers: Cluster algebras associated with extended Dynkin q…

Let Q be a Dynkin quiver of type A. The bounded derived category of the path algebra of Q has an autoequivalence given by the composition of the Auslander-Reiten translate and the square of the shift functor. We classify the maximal rigid…

In this paper the relationship between iterated tilted algebras and cluster-tilted algebras and relation-extensions is studied. In the Dynkin case, it is shown that the relationship is very strong and combinatorial.

We give an explicit description of the mutation class of quivers of type D.

For modules over an artin algebra a linear stability condition is given by a "central charge" and a nonlinear stability condition is given by the wall-crossing sequence of a "green path". Finite Harder-Narasimhan stratifications of the…

We show that for two quivers without oriented cycles related by a BGP reflection, the posets of their cluster tilting objects are related by a simple combinatorial construction, which we call a flip-flop. We deduce that the posets of…

Integral cluster categories of acyclic quivers have recently been used in the representation-theoretic approach to quantum cluster algebras. We show that over a principal ideal domain, such categories behave much better than one would…

We study the notion of positive and negative complexity of pairs of objects in cluster categories. The first main result shows that the maximal complexity occurring is either one, two or infinite, depending on the representation type of the…

We extend recent work of the third author and Kouloukas by constructing deformations of integrable cluster maps corresponding to the Dynkin types $A_{2N}$, lifting these to higher-dimensional maps possessing the Laurent property and…

We discuss degenerations of symplectic and orthogonal representations of symmetric quivers and algebras with self-dualities. As in the non-symmetric case, we define a partial ordering, that we call symmetric Ext-order which gives a…

We observe that over an algebraically closed field, any finite-dimensional algebra is the endomorphism algebra of an m-cluster-tilting object in a triangulated m-Calabi-Yau category, where m is any integer greater than 2.

Exceptional sequences are important sequences of quiver representations in the study of representation theory of algebras. They are also closely related to the theory of cluster algebras and the combinatorics of Coxeter groups. We…

Let $Q$ be a finite quiver without loops. Then there is an admissible ideal $I$ such that the algebra $kQ/I$ has global dimension at most two and is (strongly) quasi-hereditary. In addition some other (strongly) quasi-hereditary algebras…

A $d$-silting object is a silting object whose derived endomorphism algebra has global dimension $d$ or less. We give an equivalent condition, which can be stated in terms of dg quivers, for silting mutations to preserve the $d$-siltingness…

In a recent paper by K.-H. Lee, K. Lee and M. Mills, a mutation of reflections in the universal Coxeter group is defined in association with a mutation of a quiver. A matrix representation of these reflections is determined by a linear…

A cyclically ordered quiver is a quiver endowed with an additional structure of a cyclic ordering of its vertices. This structure, which naturally arises in many important applications, gives rise to new powerful mutation invariants.

Motivated by the definition of Duflo involution for fiat $2$-categories, we define certain analogues of Duflo involution for arbitrary finitary $2$-categories and show that such Duflo involutions exist for two classes of finitary…

We construct tilting modules over Jacobian algebras arising from knots. To a two-bridge knot $L[a_1,\ldots,a_n]$, we associate a quiver $Q$ with potential and its Jacobian algebra $A$. We construct a family of canonical indecomposable…

We prove that finite groups have the same complex character tables iff the group algebras are twisted forms of each other as Drinfel'd quasi-bialgebras or iff there is non-associative bi-Galois algebra over these groups. The interpretations…

Finite dimensional modular Lie superalgebras over algebraically closed fields with indecomposable Cartan matrices are classified under some technical, most probably inessential, hypotheses. If the Cartan matrix is invertible, the…

We show that Nichols algebras of most simple Yetter-Drinfeld modules over the projective symplectic linear group over a finite field, corresponding to unipotent orbits, have infinite dimension. We give a criterium to deal with unipotent…