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Cluster algebras I: Foundations

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arxiv math/0104151 v1 pith:JYRNBOGD submitted 2001-04-13 math.RT math.AGmath.QA

Sergey Fomin , Andrei Zelevinsky This is my paper · ORCID
classification math.RTmath.AGmath.QA
keywords algebrasalgebraicattemptbasescanonicalclassclustercommutative
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In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Learning to Trace Seiberg Dualities

    hep-th 2026-07 accept novelty 6.0 of 10

    Hybrid graph-transformer networks guiding A* and beam search find Seiberg-duality paths between ~10-node quivers more efficiently than BFS or pure physics heuristics, with a measured complexity breaking point.

  2. Novel cluster-algebraic letters for 5- and 6-point QCD processes

    hep-th 2026-03 conditional novelty 6.0 of 10

    Candidate symbol alphabets for 5- and 6-point QCD processes are derived from the 9-particle N=4 super Yang-Mills cluster algebra, including new nested square-root letters.

  3. Curve integral formula for the M\"obius strip

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    A global Schwinger integral is constructed for Möbius-strip amplitudes and verified against the tropical limit of the type-I superstring Möbius amplitude.

  4. Local and global patterns of rank 3 $G$-fans of totally-infinite type

    math.CO 2024-11 conditional novelty 6.0 of 10

    Infinite-type cluster algebras have G-fans that are never complete, and rank 3 local behavior falls into six types that correlate with global fan shapes.

  5. Spectral Networks: Bridging higher-rank Teichm\"uller theory and BPS states

    math-ph 2024-11 unverdicted

    A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.

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