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Bases for cluster algebras from surfaces

Part of: Algebraic combinatorics Arithmetic rings and other special rings Graph theory

Published online by Cambridge University Press:  07 December 2012

Gregg Musiker ,
Ralf Schiffler  and
Lauren Williams
Gregg Musiker
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA (email: musiker@math.umn.edu)
Ralf Schiffler
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA (email: schiffler@math.uconn.edu)
Lauren Williams
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA (email: williams@math.berkeley.edu)
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Abstract

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We construct two bases for each cluster algebra coming from a triangulated surface without punctures. We work in the context of a coefficient system coming from a full-rank exchange matrix, such as principal coefficients.

Keywords

cluster algebrabasistriangulated surfaces

MSC classification

Secondary: 13F60: Cluster algebras 05C70: Factorization, matching, partitioning, covering and packing 05E15: Combinatorial aspects of groups and algebras
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 2 , February 2013 , pp. 217 - 263
Copyright
© The Author(s) 2012

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