We generalize the construction of the bangle, band and bracelet bases for cluster algebras from unpunctured orbifolds to the case where there is only one marked point on the boundary.
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.48
Keywords: cluster algebra, unpunctured orbifold, basis, snake graph
Çanakçı, İlke 1; Tumarkin, Pavel 2
CC-BY 4.0
@article{ALCO_2019__2_3_355_0,
author = {\c{C}anak\c{c}{\i}, \.Ilke and Tumarkin, Pavel},
title = {Bases for cluster algebras from orbifolds with one marked point},
journal = {Algebraic Combinatorics},
pages = {355--365},
publisher = {MathOA foundation},
volume = {2},
number = {3},
year = {2019},
doi = {10.5802/alco.48},
zbl = {07066879},
mrnumber = {3968742},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.48/}
}
TY - JOUR AU - Çanakçı, İlke AU - Tumarkin, Pavel TI - Bases for cluster algebras from orbifolds with one marked point JO - Algebraic Combinatorics PY - 2019 SP - 355 EP - 365 VL - 2 IS - 3 PB - MathOA foundation UR - https://alco.centre-mersenne.org/articles/10.5802/alco.48/ DO - 10.5802/alco.48 LA - en ID - ALCO_2019__2_3_355_0 ER -
%0 Journal Article %A Çanakçı, İlke %A Tumarkin, Pavel %T Bases for cluster algebras from orbifolds with one marked point %J Algebraic Combinatorics %D 2019 %P 355-365 %V 2 %N 3 %I MathOA foundation %U https://alco.centre-mersenne.org/articles/10.5802/alco.48/ %R 10.5802/alco.48 %G en %F ALCO_2019__2_3_355_0
Çanakçı, İlke; Tumarkin, Pavel. Bases for cluster algebras from orbifolds with one marked point. Algebraic Combinatorics, Volume 2 (2019) no. 3, pp. 355-365. doi : 10.5802/alco.48. https://alco.centre-mersenne.org/articles/10.5802/alco.48/
[1] On cluster algebras from unpunctured surfaces with one marked point, Proc. Am. Math. Soc., Ser. B, Volume 2 (2015), pp. 35-49 | DOI | MR | Zbl
[2] Snake graph calculus and cluster algebras from surfaces, J. Algebra, Volume 382 (2013), pp. 240-281 | DOI | MR | Zbl
[3] Snake graph calculus and cluster algebras from surfaces II: self-crossing snake graphs, Math. Z., Volume 281 (2015) no. 1-2, pp. 55-102 | DOI | MR | Zbl
[4] Snake graph calculus and cluster algebras from surfaces III: band graphs and snake rings, Int. Math. Res. Not., Volume 2019 (2019) no. 4, pp. 1145-1226 | DOI | MR | Zbl
[5] Cluster algebras and triangulated orbifolds, Adv. Math., Volume 231 (2012) no. 5, pp. 2953-3002 | DOI | MR | Zbl
[6] Cluster algebras of finite mutation type via unfoldings, Int. Math. Res. Not. (2012) no. 8, pp. 1768-1804 | DOI | MR | Zbl
[7] Bases for cluster algebras from orbifolds, Adv. Math., Volume 318 (2017), pp. 191-232 | DOI | MR | Zbl
[8] Moduli spaces of local systems and higher Teichmüller theory, Publ. Math., Inst. Hautes Étud. Sci. (2006) no. 103, pp. 1-211 | DOI | Numdam | MR | Zbl
[9] Cluster algebras and triangulated surfaces. I. Cluster complexes, Acta Math., Volume 201 (2008) no. 1, pp. 83-146 | DOI | MR | Zbl
[10] Cluster algebras and triangulated surfaces Part II: Lambda lengths, Mem. Am. Math. Soc., Volume 255 (2018) no. 1223, p. v+97 | MR | Zbl
[11] Cluster algebras. I. Foundations, J. Am. Math. Soc., Volume 15 (2002) no. 2, pp. 497-529 | DOI | MR | Zbl
[12] Cluster algebras. IV. Coefficients, Compos. Math., Volume 143 (2007) no. 1, pp. 112-164 | DOI | MR | Zbl
[13] Positivity for cluster algebras from surfaces, Adv. Math., Volume 227 (2011) no. 6, pp. 2241-2308 | DOI | MR | Zbl
[14] Bases for cluster algebras from surfaces, Compos. Math., Volume 149 (2013) no. 2, pp. 217-263 | DOI | MR | Zbl
[15] Cluster algebras from surfaces: lecture notes for the CIMPA School Mar del Plata, March 2016, Homological methods, representation theory, and cluster algebras (CRM Short Courses), Springer, 2018, pp. 65-99 | DOI | MR | Zbl
[16] Positive basis for surface skein algebras, Proc. Natl. Acad. Sci. USA, Volume 111 (2014) no. 27, pp. 9725-9732 | DOI | MR | Zbl
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