Geodesic
$\mathcal{A}=\mathcal{U}$ for Locally Acyclic Cluster Algebras
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This note presents a self-contained proof that acyclic and locally acyclic cluster algebras coincide with their upper cluster algebras.
Keywords: cluster algebras; upper cluster algebras; acyclic cluster algebras. 
@article{SIGMA_2014_10_a93,
     author = {Greg Muller},
     title = {$\mathcal{A}=\mathcal{U}$ for {Locally} {Acyclic} {Cluster} {Algebras}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2014},
     volume = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a93/}
}
TY  - JOUR
AU  - Greg Muller
TI  - $\mathcal{A}=\mathcal{U}$ for Locally Acyclic Cluster Algebras
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2014
VL  - 10
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a93/
LA  - en
ID  - SIGMA_2014_10_a93
ER  - 
%0 Journal Article
%A Greg Muller
%T $\mathcal{A}=\mathcal{U}$ for Locally Acyclic Cluster Algebras
%J Symmetry, integrability and geometry: methods and applications
%D 2014
%V 10
%U http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a93/
%G en
%F SIGMA_2014_10_a93
Greg Muller. $\mathcal{A}=\mathcal{U}$ for Locally Acyclic Cluster Algebras. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a93/

[1] Berenstein A., Fomin S., Zelevinsky A., “Cluster algebras. {III}: {U}pper bounds and double {B}ruhat cells”, Duke Math. J., 126 (2005), 1–52, arXiv: math.RT/0305434 | DOI | MR | Zbl

[2] Fock V., Goncharov A., “Moduli spaces of local systems and higher {T}eichmüller theory”, Publ. Math. Inst. Hautes Études Sci., 2006, 1–211, arXiv: math.AG/0311149 | DOI | MR | Zbl

[3] Fomin S., Shapiro M., Thurston D., “Cluster algebras and triangulated surfaces. {I}: {C}luster complexes”, Acta Math., 201 (2008), 83–146, arXiv: math.RA/0608367 | DOI | MR | Zbl

[4] Fomin S., Zelevinsky A., “Cluster algebras. {I}: {F}oundations”, J. Amer. Math. Soc., 15 (2002), 497–529, arXiv: math.RT/0104151 | DOI | MR | Zbl

[5] Fomin S., Zelevinsky A., “Cluster algebras: notes for the {CDM}-03 conference”, Current Developments in Mathematics, Int. Press, Somerville, MA, 2003, 1–34, arXiv: math.RT/0311493 | DOI | MR | Zbl

[6] Fomin S., Zelevinsky A., “Cluster algebras. {IV}: {C}oefficients”, Compos. Math., 143 (2007), 112–164, arXiv: math.RA/0602259 | DOI | MR | Zbl

[7] Gekhtman M., Shapiro M., Vainshtein A., “Cluster algebras and {W}eil–{P}etersson forms”, Duke Math. J., 127 (2005), 291–311, arXiv: math.QA/0309138 | DOI | MR | Zbl

[8] Gekhtman M., Shapiro M., Vainshtein A., Cluster algebras and {P}oisson geometry, Mathematical Surveys and Monographs, 167, Amer. Math. Soc., Providence, RI, 2010 | DOI | MR | Zbl

[9] Keller B., “Cluster algebras and cluster categories”, Bull. Iranian Math. Soc., 37 (2011), 187–234 | MR | Zbl

[10] Matherne J., Muller G., “Computing upper cluster algebras”, Int. Math. Res. Not. (to appear) , arXiv: 1307.0579 | DOI

[11] Muller G., Skein algebras and cluster algebras of marked surfaces, arXiv: 1204.0020

[12] Muller G., “Locally acyclic cluster algebras”, Adv. Math., 233 (2013), 207–247, arXiv: 1111.4468 | DOI | MR | Zbl