242 citations · 546 across the 54 of their papers we have counts for
51 papers · 1 filter
A geometric realization of socle-projective categories for posets of type
Gabriel Bravo Rios, Ralf Schiffler, Robinson-Julian Serna
We introduce posets of type , a family of posets described by an admissible Dynkin quiver of type together with a compatible set of extra arrows (alien arrows), a…
On syzygy categories over Iwanaga-Gorenstein algebras: Reduction, minimality and finiteness
Ralf Schiffler, Khrystyna Serhiyenko
We study 2-Calabi-Yau tilted algebras which are non-commutative Iwanaga-Gorenstein algebras of Gorenstein dimension 1. In particular, we are interested in their syzygy categories o…
An exact structure approach to almost rigid modules over quivers of type
Thomas Brüstle, Eric J. Hanson, Sunny Roy +1
Let be the path algebra of a quiver of Dynkin type . The module category has a combinatorial model as the category of diagonals in a polygon w…
Maximal almost rigid modules over gentle algebras
Emily Barnard, Raquel Coelho Simoes, Emily Gunawan +1
We study maximal almost rigid modules over a gentle algebra . We prove that the number of indecomposable direct summands of every maximal almost rigid -module is equal to the…
On Gorenstein algebras of finite Cohen-Macaulay type: dimer tree algebras and their skew group algebras
Ralf Schiffler, Khrystyna Serhiyenko
Dimer tree algebras are a class of non-commutative Gorenstein algebras of Gorenstein dimension 1. In previous work we showed that the stable category of Cohen-Macaulay modules of a…
Knot theory and cluster algebras
Véronique Bazier-Matte, Ralf Schiffler
We establish a connection between knot theory and cluster algebras via representation theory. To every knot diagram (or link diagram), we associate a cluster algebra by constructin…
A geometric model for syzygies over 2-Calabi-Yau tilted algebras II
Ralf Schiffler, Khrystyna Serhiyenko
In this article, we continue the study of a certain family of 2-Calabi-Yau tilted algebras, called dimer tree algebras. The terminology comes from the fact that these algebras can…
A geometric model for syzygies over 2-Calabi-Yau tilted algebras
Ralf Schiffler, Khrystyna Serhiyenko
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 tr…
On the Number of -Tilting Modules over Nakayama Algebras
Hanpeng Gao, Ralf Schiffler
Let be the path algebra of the linearly oriented quiver of type with vertices modulo the -th power of the radical, and let be the path…
Tilting modules arising from knot invariants
Ralf Schiffler, David Whiting
We construct tilting modules over Jacobian algebras arising from knots. To a two-bridge knot , we associate a quiver with potential and its Jacobian algebra…
A geometric realization of socle-projective categories for posets of type
Ralf Schiffler, Robinson-Julian Serna
This paper establishes a link between the theory of cluster algebras and the theory of representations of partially ordered sets. We introduce a class of posets by requiring avoida…
Cambrian combinatorics on quiver representations (type A)
Emily Barnard, Emily Gunawan, Emily Meehan +1
This paper presents a geometric model of the Auslander-Reiten quiver of a type A quiver together with a stability function for which all indecomposable modules are stable. We also…
A note on sequential walks
Ibrahim Assem, María Julia Redondo, Ralf Schiffler
This short note is devoted to motivate and clarify the notion of sequential walk introduced by the authors in a previous work. We also give some applications of this concept.
Frieze varieties are invariant under Coxeter mutation
Kiyoshi Igusa, Ralf Schiffler
We define a generalized version of the frieze variety introduced by Lee, Li, Mills, Seceleanu and the second author. The generalized frieze variety is an algebraic variety determin…
A note on cluster automorphism groups
Wen Chang, Ralf Schiffler
We conjecture a characterization of a cluster automorphism as an algebra homomorphism from the cluster algebra to itself that restricts to a bijection between two clusters. This fo…
Frieze varieties : A characterization of the finite-tame-wild trichotomy for acyclic quivers
Kyungyong Lee, Li Li, Matthew Mills +2
We introduce a new class of algebraic varieties which we call frieze varieties. Each frieze variety is determined by an acyclic quiver. The frieze variety is defined in an elementa…
K-polynomials of type A quiver orbit closures and lacing diagrams
Ryan Kinser
This article contains an overview of the author's joint work with Allen Knutson and Jenna Rajchgot on -polynomials of orbit closures for type quivers. It is written to an au…
Group actions on cluster algebras and cluster categories
Charles Paquette, Ralf Schiffler
We introduce admissible group actions on cluster algebras, cluster categories and quivers with potential and study the resulting orbit spaces. The orbit space of the cluster algebr…
Modules over cluster-tilted algebras that do not lie on local slices
Ibrahim Assem, Ralf Schiffler, Khrystyna Serhiyenko
We characterize the indecomposable transjective modules over an arbitrary cluster-tilted algebra that do not lie on a local slice, and we provide a sharp upper bound for the number…
Cluster-tilted and quasi-tilted algebras
Ibrahim Assem, Ralf Schiffler, Khrystyna Serhiyenko
In this paper, we prove that relation-extensions of quasi-tilted algebras are 2-Calabi-Yau tilted. With the objective of describing the module category of a cluster-tilted algebra…
Injective Presentations of Induced Modules over Cluster-Tilted Algebras
Ralf Schiffler, Khrystyna Serhiyenko
Every cluster-tilted algebra is the relation extension of a tilted algebra . A -module is called induced if it is of the form $M\otimes_C…
On syzygies over 2-Calabi-Yau tilted algebras
Ana Garcia Elsener, Ralf Schiffler
We characterize the syzygies and co-syzygies over 2-Calabi-Yau tilted algebras in terms of the Auslander-Reiten translation and the syzygy functor. We explore connections between t…
Hochschild cohomology of relation extension algebras
Ibrahim Assem, M. Andrea Gatica, Ralf Schiffler +1
Let be the split extension of a finite dimensional algebra by a --bimodule . We define a morphism of associative graded algebras $φ^*:\HH^*(B)\rightarrow \HH^*(C)$…
Induced and Coinduced Modules in Cluster-Tilted Algebras
Ralf Schiffler, Khrystyna Serhiyenko
We propose a new approach to study the relation between the module categories of a tilted algebra and the corresponding cluster-tilted algebra . This new approach…