scholarly journals Frobenius degenerations of preprojective algebras

2020 ◽  
Vol 14 (1) ◽  
pp. 349-411
Author(s):  
Daniel Kaplan
Keyword(s):  
Preprojective Algebras

scholarly journals On central extensions of preprojective algebras

2007 ◽  
Vol 313 (1) ◽  
pp. 165-175 ◽  
Author(s):  
Pavel Etingof ◽  
Frédéric Latour ◽  
Eric Rains
Keyword(s):  
Central Extensions ◽  
Preprojective Algebras

scholarly journals On Hochschild Cohomology of Preprojective Algebras, I

1998 ◽  
Vol 205 (2) ◽  
pp. 391-412 ◽  
Author(s):  
Karin Erdmann ◽  
Nicole Snashall
Keyword(s):  
Hochschild Cohomology ◽  
Preprojective Algebras

scholarly journals Semicanonical bases and preprojective algebras

2005 ◽  
Vol 38 (2) ◽  
pp. 193-253 ◽  
Author(s):  
C GEISS ◽  
B LECLERC ◽  
J SCHROER
Keyword(s):  
Preprojective Algebras

scholarly journals Cluster structures for 2-Calabi–Yau categories and unipotent groups

2009 ◽  
Vol 145 (4) ◽  
pp. 1035-1079 ◽  
Author(s):  
A. B. Buan ◽  
O. Iyama ◽  
I. Reiten ◽  
J. Scott
Keyword(s):  
Cluster Structure ◽  
Cluster Algebras ◽  
New Class ◽  
Preprojective Algebras ◽  
Unipotent Groups ◽  
Special Cases ◽  
Dynkin Quivers ◽  
Cluster Tilting ◽  
Stable Categories ◽  
Tilting Objects

AbstractWe investigate cluster-tilting objects (and subcategories) in triangulated 2-Calabi–Yau and related categories. In particular, we construct a new class of such categories related to preprojective algebras of non-Dynkin quivers associated with elements in the Coxeter group. This class of 2-Calabi–Yau categories contains, as special cases, the cluster categories and the stable categories of preprojective algebras of Dynkin graphs. For these 2-Calabi–Yau categories, we construct cluster-tilting objects associated with each reduced expression. The associated quiver is described in terms of the reduced expression. Motivated by the theory of cluster algebras, we formulate the notions of (weak) cluster structure and substructure, and give several illustrations of these concepts. We discuss connections with cluster algebras and subcluster algebras related to unipotent groups, in both the Dynkin and non-Dynkin cases.

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