1,720,966 research outputs found
Acyclic cluster algebras with dense -vector fans
Get PDFThe -vector fans play an important role in studying cluster algebras and silting theory. We survey cluster algebras with dense -vector fans and show that a connected acyclic cluster algebra has a dense -vector fan if and only if it is either finite type or affine type. As an application, we classify finite dimensional hereditary algebras with dense -vector fans.23 page
Wide subcategories are semistable
Get PDFFor an arbitrary finite dimensional algebra , we prove that any wide
subcategory of satisfying a certain finiteness condition
is -semistable for some stability condition . More generally,
we show that wide subcategories of associated with
two-term presilting complexes of are semistable. This provides a
complement for Ingalls-Thomas-type bijections for finite dimensional algebras.Comment: 8 page
Dimension vectors of -rigid modules and -vectors of cluster monomials from triangulated surfaces
Get PDFFor the cluster algebra associated with a triangulated surface, we give a characterization of the triangulated surface such that different non-initial cluster monomials in have different -vectors. Similarly, for the associated Jacobian algebra , we give a characterization of the triangulated surface such that different -rigid -modules have different dimension vectors. Moreover, we also show that different basic support -tilting -modules have different dimension vectors. Our main ingredient is a notion of intersection numbers defined by Qiu and Zhou. As an application, we show that the denominator conjecture holds for if the marked surface is a closed surface with exactly one puncture, or the given tagged triangulation has neither loops nor tagged arcs connecting punctures.45 page
Denominator vectors and dimension vectors from triangulated surfaces
Get PDFIn a categorification of skew-symmetric cluster algebras, each cluster variable corresponds with an indecomposable module over the associated Jacobian algebra. Buan, Marsh and Reiten studied when the denominator vector of each cluster variable in an acyclic cluster algebra coincides with the dimension vector of the corresponding module. In this paper, we give analogues of their results for cluster algebras from triangulated surfaces by comparing two kinds of intersection numbers of tagged arcs.20 pages, v2: minor correction
Denseness of -vector cones from weighted orbifolds
Get PDFWe study -vector cones in a cluster algebra defined from a weighted
orbifold of rank introduced by Felikson, Shapiro and Tumarkin. We determine
the closure of the union of the -vector cones. It is equal to
except for a weighted orbifold with empty boundary and exactly one puncture, in
which case it is equal to the half space of a certain explicit hyperplane in
.Comment: 21 pages. this article draws heavily from arXiv:1904.12479, v2: minor
correction
Combinatorial cluster expansion formulas from triangulated surfaces
Get PDFWe give a cluster expansion formula for cluster algebras with principal coefficients defined from triangulated surfaces in terms of perfect matchings of angles. Our formula simplifies the cluster expansion formula given by Musiker-Schiffler-Williams in terms of perfect matchings of snake graphs. A key point of our proof is to give a bijection between perfect matchings of angles in some triangulated polygon and perfect matchings of the corresponding snake graph. Moreover, they also correspond bijectively with perfect matchings of the corresponding bipartite graph and minimal cuts of the corresponding quiver with potential.31 page
Erratum to: Tame Algebras Have Dense g-Vector Fans
No full textInternational audienceWhen this paper first published online, it contained a number of errors, which have nowbeen corrected online.The original paper did not clearly state that Pierre-Guy Plamondon and ToshiyaYurikusa were the author of the paper, but that Bernhard Keller was the author of theappendix.A dedication to the memory of Andrzej Skowronski was missin
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
-matrices of cluster algebras from triangulated surfaces
Get PDFFor a given marked surface and a fixed tagged triangulation of
, we show that each tagged triangulation of is uniquely
determined by the intersection numbers of tagged arcs of and tagged arcs of
. As consequence, each cluster in the cluster algebra is
uniquely determined by its -matrix which is a new numerical invariant of the
cluster introduced by Fujiwara and Gyoda.Comment: 33 page
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