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This article is cited in 3 scientific papers (total in 3 papers)
A $\tau$-Tilting Approach to Dissections of Polygons
Vincent Pilauda, Pierre-Guy Plamondonb, Salvatore Stellac a CNRS & LIX, École Polytechnique, Palaiseau, France
b Laboratoire de Mathématiques d'Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, France
c University of Haifa, Israel
Abstract:
We show that any accordion complex associated to a dissection of a convex polygon is isomorphic to the support $\tau$-tilting simplicial complex of an explicit finite dimensional algebra. To this end, we prove a property of some induced subcomplexes of support $\tau$-tilting simplicial complexes of finite dimensional algebras.
Keywords:
dissections of polygons; accordion complexes; $\tau$-tilting theory; representations of finite dimensional algebras; $\mathbf{g}$-vectors.
Received: February 26, 2018; in final form May 10, 2018; Published online May 14, 2018
Citation:
Vincent Pilaud, Pierre-Guy Plamondon, Salvatore Stella, “A $\tau$-Tilting Approach to Dissections of Polygons”, SIGMA, 14 (2018), 045, 8 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1344 https://www.mathnet.ru/eng/sigma/v14/p45
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