scholarly journals Representation type via Euler characteristics and singularities of quiver Grassmannians

2019 ◽  
Vol 51 (5) ◽  
pp. 815-835
Author(s):  
Oliver Lorscheid ◽  
Thorsten Weist
Keyword(s):  
Representation Type ◽  
Euler Characteristics ◽  
Quiver Grassmannians

scholarly journals Quiver Grassmannians of Type $\widetilde {D}_{n}$, Part 2: Schubert Decompositions and F-polynomials

2021 ◽  
Author(s):  
Oliver Lorscheid ◽  
Thorsten Weist
Keyword(s):  
Cluster Algebras ◽  
Indecomposable Representation ◽  
Euler Characteristics ◽  
Affine Spaces ◽  
Quiver Grassmannians ◽  
Small Defect ◽  
Quiver Grassmannian ◽  
Vertex Set ◽  
Explicit Formulae ◽  
Fixed Tree

AbstractExtending the main result of Lorscheid and Weist (2015), in the first part of this paper we show that every quiver Grassmannian of an indecomposable representation of a quiver of type $\tilde D_{n}$ D ~ n has a decomposition into affine spaces. In the case of real root representations of small defect, the non-empty cells are in one-to-one correspondence to certain, so called non-contradictory, subsets of the vertex set of a fixed tree-shaped coefficient quiver. In the second part, we use this characterization to determine the generating functions of the Euler characteristics of the quiver Grassmannians (resp. F-polynomials). Along these lines, we obtain explicit formulae for all cluster variables of cluster algebras coming from quivers of type $\tilde D_{n}$ D ~ n .

scholarly journals Cell decompositions and algebraicity of cohomology for quiver Grassmannians

2021 ◽  
Vol 379 ◽  
pp. 107544
Author(s):  
Giovanni Cerulli Irelli ◽  
Francesco Esposito ◽  
Hans Franzen ◽  
Markus Reineke
Keyword(s):  
Quiver Grassmannians ◽  
Cell Decompositions

scholarly journals Euler characteristics in the quantum K-theory of flag varieties

2020 ◽  
Vol 26 (2) ◽  
Author(s):  
Anders S. Buch ◽  
Sjuvon Chung ◽  
Changzheng Li ◽  
Leonardo C. Mihalcea
Keyword(s):  
Flag Varieties ◽  
Euler Characteristics ◽  
K Theory

CLOSE NEIGHBORS IN THE QUIVER OF TILTING MODULES

2008 ◽  
Vol 07 (03) ◽  
pp. 379-392
Author(s):  
DIETER HAPPEL
Keyword(s):  
Representation Type ◽  
Tilting Module ◽  
Tilting Modules ◽  
Hereditary Algebra ◽  
Simple Modules ◽  
Finite Dimensional ◽  
Wild Representation Type ◽  
Local Properties

For a finite dimensional hereditary algebra Λ local properties of the quiver [Formula: see text] of tilting modules are investigated. The existence of special neighbors of a given tilting module is shown. If Λ has more than 3 simple modules it is shown as an application that Λ is of wild representation type if and only if [Formula: see text] is a subquiver of [Formula: see text].

REPRESENTATION TYPE OF   H1 

2005 ◽  
Vol 57 (3) ◽  
pp. 319-338
Author(s):  
Y. Drozd
Keyword(s):  
Representation Type
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