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Cartan matrices of selfinjective algebras of tubular type

Jerzy Białkowski (2004)

Open Mathematics

The Cartan matrix of a finite dimensional algebra A is an important combinatorial invariant reflecting frequently structural properties of the algebra and its module category. For example, one of the important features of the modular representation theory of finite groups is the nonsingularity of Cartan matrices of the associated group algebras (Brauer’s theorem). Recently, the class of all tame selfinjective algebras having simply connected Galois coverings and the stable Auslander-Reiten quiver...

Classification of discrete derived categories

Grzegorz Bobiński, Christof Geiß, Andrzej Skowroński (2004)

Open Mathematics

The main aim of the paper is to classify the discrete derived categories of bounded complexes of modules over finite dimensional algebras.

Classification of low-dimensional orbit closures in varieties of quiver representations

Paweł Rochman (2008)

Colloquium Mathematicae

We classify the affine varieties of dimension at most 4 which occur as orbit closures with an invariant point in varieties of representations of quivers. Moreover, we show that they are normal and Cohen-Macaulay.

Cluster categories for algebras of global dimension 2 and quivers with potential

Claire Amiot (2009)

Annales de l’institut Fourier

Let $k$ be a field and $A$ a finite-dimensional $k$ -algebra of global dimension $\leq 2$ . We construct a triangulated category $𝒞_{A}$ associated to $A$ which, if $A$ is hereditary, is triangle equivalent to the cluster category of $A$ . When $𝒞_{A}$ is Hom-finite, we prove that it is 2-CY and endowed with a canonical cluster-tilting object. This new class of categories contains some of the stable categories of modules over a preprojective algebra studied by Geiss-Leclerc-Schröer and by Buan-Iyama-Reiten-Scott. Our results also...

Cluster characters for 2-Calabi–Yau triangulated categories

Yann Palu (2008)

Annales de l’institut Fourier

Starting from an arbitrary cluster-tilting object $T$ in a 2-Calabi–Yau triangulated category over an algebraically closed field, as in the setting of Keller and Reiten, we define, for each object $L$ , a fraction $X (T, L)$ using a formula proposed by Caldero and Keller. We show that the map taking $L$ to $X (T, L)$ is a cluster character, i.e. that it satisfies a certain multiplication formula. We deduce that it induces a bijection, in the finite and the acyclic case, between the indecomposable rigid objects of the cluster...

Coalgebras, comodules, pseudocompact algebras and tame comodule type

Daniel Simson (2001)

Colloquium Mathematicae

We develop a technique for the study of K-coalgebras and their representation types by applying a quiver technique and topologically pseudocompact modules over pseudocompact K-algebras in the sense of Gabriel [17], [19]. A definition of tame comodule type and wild comodule type for K-coalgebras over an algebraically closed field K is introduced. Tame and wild coalgebras are studied by means of their finite-dimensional subcoalgebras. A weak version of the tame-wild dichotomy theorem of Drozd [13]...

Cohomology of algebras of dihedral type. I.

Generalov, A.I. (2002)

Zapiski Nauchnykh Seminarov POMI

Cohomology of algebras of semidihedral type. IV.

Generalov, A.I. (2004)

Zapiski Nauchnykh Seminarov POMI

Combinatorial interpretations for rank-two cluster algebras of affine type.

Musiker, Gregg, Propp, James (2007)

The Electronic Journal of Combinatorics [electronic only]

Comments on gentleness of endomorphism algebras.

Zimmermann, Alexander (2003)

AMA. Algebra Montpellier Announcements [electronic only]

Component clusters for acyclic quivers

Sarah Scherotzke (2016)

Colloquium Mathematicae

The theory of Caldero-Chapoton algebras of Cerulli Irelli, Labardini-Fragoso and Schröer (2015) leads to a refinement of the notions of cluster variables and clusters, via so-called component clusters. We compare component clusters to classical clusters for the cluster algebra of an acyclic quiver. We propose a definition of mutation between component clusters and determine the mutation relations of component clusters for affine quivers. In the case of a wild quiver, we provide bounds for the size...

Consistent algebras and special tilting sequences.

Lutz Hille (1995)

Mathematische Zeitschrift

Constructing the directing components of an algebra

J. de la Peña, M. Takane (1997)

Colloquium Mathematicae

Coordinates of maximal roots of weakly non-negative unit forms

P. Dräxler, N. Golovachtchuk, S. Ovsienko, J. de la Pena (1998)

Colloquium Mathematicae

Counting the number of elements in the mutation classes of $A_{n}$ -quivers.

Bastian, Janine, Prellberg, Thomas, Rubey, Martin, Stump, Christian (2011)

The Electronic Journal of Combinatorics [electronic only]

Coxeter polynomials of Salem trees

Charalampos A. Evripidou (2015)

Colloquium Mathematicae

We compute the Coxeter polynomial of a family of Salem trees, and also the limit of the spectral radii of their Coxeter transformations as the number of their vertices tends to infinity. We also prove that if z is a root of multiplicities $m ₁, . . ., m_{k}$ for the Coxeter polynomials of the trees $₁, . . .,_{k}$ respectively, then z is a root for the Coxeter polynomial of their join, of multiplicity at least $m i n m - m ₁, . . ., m - m_{k}$ where $m = m ₁ + \dots + m_{k}$ .

Currently displaying 1 – 16 of 16

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