Vincent Pilaud, Pierre-Guy Plamondon, Salvatore Stella, “A $\tau$-Tilting Approach to Dissections of Polygons”, SIGMA, 14 (2018), 045, 8 pp.

Symmetry, Integrability and Geometry: Methods and Applications

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Symmetry, Integrability and Geometry: Methods and Applications, 2018, Volume 14, 045, 8 pp.
DOI: https://doi.org/10.3842/SIGMA.2018.045 (Mi sigma1344)

This article is cited in 3 scientific papers (total in 3 papers)

A

τ

$\tau$ -Tilting Approach to Dissections of Polygons

Vincent Pilaud^a, Pierre-Guy Plamondon^b, 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

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DOI: https://doi.org/10.3842/SIGMA.2018.045

Abstract: We show that any accordion complex associated to a dissection of a convex polygon is isomorphic to the support

τ

$\tau$ -tilting simplicial complex of an explicit finite dimensional algebra. To this end, we prove a property of some induced subcomplexes of support

τ

$\tau$ -tilting simplicial complexes of finite dimensional algebras.

Keywords: dissections of polygons; accordion complexes;

τ

$\tau$ -tilting theory; representations of finite dimensional algebras;

g

$\mathbf{g}$ -vectors.

Funding agency	Grant number
Agence Nationale de la Recherche	SC3A (15 CE40 0004 01)
Israel Science Foundation	1144/16
The first two authors are partially supported by the French ANR grant SC3A (15 CE40 0004 01). The last author is supported by the ISF grant 1144/16.

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

Bibliographic databases:

Document Type: Article

MSC: 16G10; 16G20; 05E10

Language: English

Citation: Vincent Pilaud, Pierre-Guy Plamondon, Salvatore Stella, “A

τ

$\tau$ -Tilting Approach to Dissections of Polygons”, SIGMA, 14 (2018), 045, 8 pp.

Citation in format AMSBIB

\Bibitem{PilPlaSte18}

\by Vincent~Pilaud, Pierre-Guy~Plamondon, Salvatore~Stella

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

\jour SIGMA

\yr 2018

\vol 14

\papernumber 045

\totalpages 8

\mathnet{http://mi.mathnet.ru/sigma1344}

\crossref{https://doi.org/10.3842/SIGMA.2018.045}

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Linking options:

https://www.mathnet.ru/eng/sigma1344

https://www.mathnet.ru/eng/sigma/v14/p45

This publication is cited in the following 3 articles:

Y. Palu, V. Pilaud, P.-G. Plamondon, Non-kissing complexes and tau-tilting for gentle algebras introduction, Mem. Am. Math. Soc., 274, no. 1343, 2021
P.-G. Plamondon, “Tau-tilting finite gentle algebras are representation-finite”, Pac. J. Math., 302:2 (2019), 709–716
Ya. Palu, V. Pilaud, P.-G. Plamondon, “Non-kissing and non-crossing complexes for locally gentle algebras”, J. Comb. Algebra, 3:4 (2019), 401–438

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Symmetry, Integrability and Geometry: Methods and Applications

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Full-text PDF :	415
References:	32

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