Snake graph calculus and cluster algebras from surfaces

Ilke Canakci; Ralf Schiffler

doi:10.1016/j.jalgebra.2013.02.018

Snake graph calculus and cluster algebras from surfaces

Ilke Canakci, Ralf Schiffler^*

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

Snake graphs appear naturally in the theory of cluster algebras. For cluster algebras from surfaces, each cluster variable is given by a formula which is parametrized by the perfect matchings of a snake graph. In this paper, we identify each cluster variable with its snake graph, and interpret relations among the cluster variables in terms of these graphs. In particular, we give a new proof of skein relations of two cluster variables.

Original language	English
Pages (from-to)	240-281
Number of pages	42
Journal	Journal of Algebra
Volume	382
DOIs	https://doi.org/10.1016/j.jalgebra.2013.02.018
Publication status	Published - 5 May 2013
Externally published	Yes

Funding

✩ The authors were supported by the NSF grant DMS-1001637 and by the University of Connecticut.

Keywords

Cluster algebras from surfaces
Cluster variables
Perfect matchings
Skein relations
Snake graphs

Access to Document

10.1016/j.jalgebra.2013.02.018

Persistent URL (handle)

Persistent link

Cite this

@article{a591a574de96478992f40472c426afd4,

title = "Snake graph calculus and cluster algebras from surfaces",

abstract = "Snake graphs appear naturally in the theory of cluster algebras. For cluster algebras from surfaces, each cluster variable is given by a formula which is parametrized by the perfect matchings of a snake graph. In this paper, we identify each cluster variable with its snake graph, and interpret relations among the cluster variables in terms of these graphs. In particular, we give a new proof of skein relations of two cluster variables.",

keywords = "Cluster algebras from surfaces, Cluster variables, Perfect matchings, Skein relations, Snake graphs",

author = "Ilke Canakci and Ralf Schiffler",

year = "2013",

month = may,

day = "5",

doi = "10.1016/j.jalgebra.2013.02.018",

language = "English",

volume = "382",

pages = "240--281",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Snake graph calculus and cluster algebras from surfaces

AU - Canakci, Ilke

AU - Schiffler, Ralf

PY - 2013/5/5

Y1 - 2013/5/5

N2 - Snake graphs appear naturally in the theory of cluster algebras. For cluster algebras from surfaces, each cluster variable is given by a formula which is parametrized by the perfect matchings of a snake graph. In this paper, we identify each cluster variable with its snake graph, and interpret relations among the cluster variables in terms of these graphs. In particular, we give a new proof of skein relations of two cluster variables.

AB - Snake graphs appear naturally in the theory of cluster algebras. For cluster algebras from surfaces, each cluster variable is given by a formula which is parametrized by the perfect matchings of a snake graph. In this paper, we identify each cluster variable with its snake graph, and interpret relations among the cluster variables in terms of these graphs. In particular, we give a new proof of skein relations of two cluster variables.

KW - Cluster algebras from surfaces

KW - Cluster variables

KW - Perfect matchings

KW - Skein relations

KW - Snake graphs

UR - http://www.scopus.com/inward/record.url?scp=84875260410&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84875260410&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2013.02.018

DO - 10.1016/j.jalgebra.2013.02.018

M3 - Article

AN - SCOPUS:84875260410

SN - 0021-8693

VL - 382

SP - 240

EP - 281

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Snake graph calculus and cluster algebras from surfaces

Abstract

Funding

Keywords

Access to Document

Persistent URL (handle)

Other files and links

Fingerprint

Cite this