Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 045, 8 pages      arXiv:1710.02119

A $\tau$-Tilting Approach to Dissections of Polygons

Vincent Pilaud a, Pierre-Guy Plamondon b and Salvatore Stella c
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

Received February 26, 2018, in final form May 10, 2018; Published online May 14, 2018

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.

Key words: dissections of polygons; accordion complexes; $\tau$-tilting theory; representations of finite dimensional algebras; $\mathbf{g}$-vectors.

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