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

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

12 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
Externally published	Yes

Keywords

Invariant theory
Quiver mutation
Tensor diagram

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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.",

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AU - Fomin, Sergey

AU - Pylyavskyy, Pavlo

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KW - Invariant theory

KW - Quiver mutation

KW - Tensor diagram

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DO - 10.1073/pnas.1313068111

M3 - Review article

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

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Webs on surfaces, rings of invariants, and clusters

Abstract

Keywords

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