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Proceedings of the American Mathematical Society Series B

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On cluster algebras from unpunctured surfaces with one marked point


Authors: Ilke Canakci, Kyungyong Lee and Ralf Schiffler
Journal: Proc. Amer. Math. Soc. Ser. B 2 (2015), 35-49
MSC (2010): Primary 13F60
DOI: https://doi.org/10.1090/bproc/21
Published electronically: November 13, 2015
MathSciNet review: 3422667
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Abstract: We extend the construction of canonical bases for cluster algebras from unpunctured surfaces to the case where the number of marked points on the boundary is one. We show that the cluster algebra is equal to the upper cluster algebra in this case.


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Additional Information

Ilke Canakci
Affiliation: Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom
Address at time of publication: Department of Mathematical Sciences, Durham University, Lower Mountjoy, Stockton Road, Durham DH1 3LE, United Kingdom
Email: ilke.canakci@durham.ac.uk

Kyungyong Lee
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202 — and — Center for Mathematical Challenges, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722, Republic of Korea
Address at time of publication: Department of Mathematics, University of Nebraska-Lincoln, 210 Avery Hall, Lincoln, NE 68588-0130, USA
Email: klee24@unl.edu, klee1@kias.re.kr

Ralf Schiffler
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269-3009
Email: schiffler@math.uconn.edu

DOI: https://doi.org/10.1090/bproc/21
Keywords: Cluster algebra, upper cluster algebra, unpunctured surface, basis
Received by editor(s): August 23, 2014
Published electronically: November 13, 2015
Additional Notes: The first author was supported by EPSRC grant number EP/K026364/1, UK and the University of Leicester
The second author was supported by Wayne State University, the Korea Institute for Advanced Study, AMS Centennial Fellowship and NSA grant H98230-14-1-0323
The third author was supported by NSF grants DMS-1254567, DMS-1101377 and by the University of Connecticut
Communicated by: Harm Derksen
Article copyright: © Copyright 2015 by the author under Creative Commons Attribution 3.0 License (CC BY 3.0)

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