Geodesic
Semistable Subcategories for Tiling Algebras
Séminaire lotharingien de combinatoire, 80B (2018)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

Semistable subcategories were introduced in the context of Mumford's GIT and interpreted by King in terms of representation theory of finite dimensional algebras. Ingalls and Thomas later showed that for finite dimensional algebras of Dynkin and affine type, the poset of semistable subcategories is isomorphic to the corresponding lattice of noncrossing partitions. We show that semistable subcategories defined by tiling algebras, introduced by Sim{\~o}es and Parsons, are in bijection with noncrossing tree partitions, introduced by the second author and McConville. Our work recovers that of Ingalls and Thomas in Dynkin type A. 

@article{SLC_2018_80B_a21,
     author = {Monica Garcia and Alexander Garver},
     title = {Semistable {Subcategories} for {Tiling} {Algebras}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a21/}
}
TY  - JOUR
AU  - Monica Garcia
AU  - Alexander Garver
TI  - Semistable Subcategories for Tiling Algebras
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a21/
ID  - SLC_2018_80B_a21
ER  - 
%0 Journal Article
%A Monica Garcia
%A Alexander Garver
%T Semistable Subcategories for Tiling Algebras
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a21/
%F SLC_2018_80B_a21
Monica Garcia; Alexander Garver. Semistable Subcategories for Tiling Algebras. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a21/