Deep Points of Cluster Algebras

Abstract We initiate a systematic study of the deep points of a cluster algebra; that is, the points in the associated variety which are not in any cluster torus. We describe the deep points of cluster algebras of type A, rank 2, Markov, and unpunctured surface type.

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Publication Details

Journal
International Mathematics Research Notices
Published
2025-01-28
DOI
https://doi.org/10.1093/imrn/rnaf027
Primary Topic
Algebraic structures and combinatorial models
Type
article
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article

Deep Points of Cluster Algebras

Greg Muller, James C. Beyer
International Mathematics Research Notices
Algebraic structures and combinatorial models
article

Deep Points of Cluster Algebras

Greg Muller, James C. Beyer
article en

Abstract

Abstract We initiate a systematic study of the deep points of a cluster algebra; that is, the points in the associated variety which are not in any cluster torus. We describe the deep points of cluster algebras of type A, rank 2, Markov, and unpunctured surface type.

International Mathematics Research NoticesVol. 2025(4)
University of Oklahoma (US)
Openalex Percentile: Top 74%
Algebraic structures and combinatorial models
DOIOpen Access PDFOpenAlex
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Deep Points of Cluster Algebras — Greg Muller, James C. Beyer · International Mathematics Research Notices (2025) | TGRS Research Map | TGRS