Webs on surfaces, rings of invariants, and clusters

Sergey Fomin; Pavlo Pylyavskyy

doi:10.1073/pnas.1313068111

Webs on surfaces, rings of invariants, and clusters

Sergey Fomin, Pavlo Pylyavskyy

School of Mathematics

Research output: Contribution to journal › Review article › peer-review

13 Scopus citations

Abstract

We construct and study cluster algebra structures in rings of invariants of the special linear group action on collections of 3D vectors, covectors, and matrices. The construction uses Kuperberg's calculus of webs on marked surfaces with boundary.

Original language	English (US)
Pages (from-to)	9680-9687
Number of pages	8
Journal	Proceedings of the National Academy of Sciences of the United States of America
Volume	111
Issue number	27
DOIs	https://doi.org/10.1073/pnas.1313068111
State	Published - Jul 8 2014

Keywords

Invariant theory
Quiver mutation
Tensor diagram

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10.1073/pnas.1313068111

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title = "Webs on surfaces, rings of invariants, and clusters",

abstract = "We construct and study cluster algebra structures in rings of invariants of the special linear group action on collections of 3D vectors, covectors, and matrices. The construction uses Kuperberg's calculus of webs on marked surfaces with boundary.",

keywords = "Invariant theory, Quiver mutation, Tensor diagram",

author = "Sergey Fomin and Pavlo Pylyavskyy",

year = "2014",

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doi = "10.1073/pnas.1313068111",

language = "English (US)",

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T1 - Webs on surfaces, rings of invariants, and clusters

AU - Fomin, Sergey

AU - Pylyavskyy, Pavlo

PY - 2014/7/8

Y1 - 2014/7/8

N2 - We construct and study cluster algebra structures in rings of invariants of the special linear group action on collections of 3D vectors, covectors, and matrices. The construction uses Kuperberg's calculus of webs on marked surfaces with boundary.

AB - We construct and study cluster algebra structures in rings of invariants of the special linear group action on collections of 3D vectors, covectors, and matrices. The construction uses Kuperberg's calculus of webs on marked surfaces with boundary.

KW - Invariant theory

KW - Quiver mutation

KW - Tensor diagram

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U2 - 10.1073/pnas.1313068111

DO - 10.1073/pnas.1313068111

M3 - Review article

AN - SCOPUS:84903954489

SN - 0027-8424

VL - 111

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EP - 9687

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 27

ER -

Webs on surfaces, rings of invariants, and clusters

Abstract

Keywords

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