Séminaire Lotharingien de Combinatoire, 80B.22 (2018), 12 pp.
Monica
Garcia and Alexander
Garver
Semistable Subcategories for Tiling Algebras
Abstract.
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.
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
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