Quivers with relations for symmetrizable Cartan matrices V: Caldero-Chapoton formulas
نویسندگان
چکیده
منابع مشابه
The Caldero–Chapoton formula for cluster algebras
In this article, we state the necessary background for cluster algebras and quiver representations to formulate and prove a result of Caldero and Chapoton which gives a nice formula connecting the two subjects. In our exposition, we mostly follow the paper [CC], but we have tried to minimize the reliance of citing outside sources as much as possible. In particular, we avoid having to introduce ...
متن کاملAlgorithms and Properties for Positive Symmetrizable Matrices
Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating symmetrizable matrices with specific characteristics, called positive quasi-Cartan companion matrices. Here, symmetrizable matrix are those which are symmetric when m...
متن کاملGeneralised Friezes and a Modified Caldero-chapoton Map Depending on a Rigid Object
The (usual) Caldero-Chapoton map is a map from the set of objects of a category to a Laurent polynomial ring over the integers. In the case of a cluster category, it maps “reachable” indecomposable objects to the corresponding cluster variables in a cluster algebra. This formalises the idea that the cluster category is a “categorification” of the cluster algebra. The definition of the Caldero-C...
متن کاملGeneric Representation Theory of Quivers with Relations
Let Λ be a basic finite dimensional algebra over an algebraically closed field K. Tameness of the representation type of Λ – the only situation in which one can, at least in principle, meaningfully classify all finite dimensional representations of Λ – is a borderline phenomenon. However, even in the wild scenario, it is often possible to obtain a good grasp of the “bulk” of d-dimensional repre...
متن کاملExponent matrices and their quivers
Exponent matrices appeared in the study of tiled orders over discrete valuation rings. Many properties of such orders are formulated using this notion. We think that such matrices are of interest in them own right, in particular, it is convenient to write finite partially ordered sets (posets) and finite metric spaces as special exponent matrices. Note that when we defined a quiver Q(E) of a re...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2018
ISSN: 0024-6115
DOI: 10.1112/plms.12146