EXCEPTIONAL SEQUENCES FOR QUIVERS OF DYNKIN TYPE

2001 ◽  
Vol 29 (3) ◽  
pp. 1373-1386 ◽  
Author(s):  
Uwe Seidel
Keyword(s):  
Dynkin Type ◽  
Exceptional Sequences

τ-exceptional sequences

2021 ◽  
Author(s):  
Aslak Bakke Buan ◽  
Bethany Rose Marsh
Keyword(s):  
Exceptional Sequences

scholarly journals Quotients of cluster categories

2010 ◽  
Vol 140 (1) ◽  
pp. 65-81 ◽  
Author(s):  
Peter Jørgensen
Keyword(s):  
The Other ◽  
Dynkin Type ◽  
Cluster Categories

Higher cluster categories were recently introduced as a generalization of cluster categories. This paper shows that in Dynkin types A and D, half of all higher cluster categories can be obtained as quotients of cluster categories. The other half are quotients of 2-cluster categories, the ‘lowest’ type of higher cluster categories. Hence, in Dynkin types A and D, all higher cluster phenomena are implicit in cluster categories and 2-cluster categories. In contrast, the same is not true in Dynkin type E.

scholarly journals Combinatorics of Exceptional Sequences in Type A

10.37236/6251 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Alexander Garver ◽  
Kiyoshi Igusa ◽  
Jacob P. Matherne ◽  
Jonah Ostroff
Keyword(s):  
Dynkin Diagram ◽  
Type A ◽  
Linear Extensions ◽  
Quiver Representations ◽  
Noncrossing Partitions ◽  
Underlying Graph ◽  
Exceptional Sequences

Exceptional sequences are certain sequences of quiver representations.  We introduce a class of objects called strand diagrams and use these to classify exceptional sequences of representations of a quiver whose underlying graph is a type $\mathbb{A}_n$ Dynkin diagram. We also use variations of these objects to classify $c$-matrices of such quivers, to interpret exceptional sequences as linear extensions of explicitly constructed posets, and to give a simple bijection between exceptional sequences and certain saturated chains in the lattice of noncrossing partitions. 

scholarly journals From m-clusters to m-noncrossing partitions via exceptional sequences

2011 ◽  
Vol 271 (3-4) ◽  
pp. 1117-1139 ◽  
Author(s):  
Aslak Bakke Buan ◽  
Idun Reiten ◽  
Hugh Thomas
Keyword(s):  
Noncrossing Partitions ◽  
Exceptional Sequences

A Graph Theoretical Framework for the Strong Gram Classification of Non-negative Unit Forms of Dynkin Type 𝔸n

2022 ◽  
Vol 184 (1) ◽  
pp. 49-82
Author(s):  
Jesús Arturo Jiménez González
Keyword(s):  
Theoretical Framework ◽  
Line Graphs ◽  
Positive Unit ◽  
Dynkin Type ◽  
Principal Unit

In the context of signed line graphs, this article introduces a modified inflation technique to study strong Gram congruence of non-negative (integral quadratic) unit forms, and uses it to show that weak and strong Gram congruence coincide among positive unit forms of Dynkin type 𝔸n. The concept of inverse of a quiver is also introduced, and is used to obtain and analyze the Coxeter matrix of non-negative unit forms of Dynkin type 𝔸n. With these tools, connected principal unit forms of Dynkin type 𝔸n are also classified up to strong congruence.

Deformed mesh algebras of Dynkin type Cn

2012 ◽  
Vol 126 (2) ◽  
pp. 217-230 ◽  
Author(s):  
Jerzy Białkowski ◽  
Karin Erdmann ◽  
Andrzej Skowroński
Keyword(s):  
Dynkin Type
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