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Introduction to Cluster Algebras. Chapter 6

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arxiv 2008.09189 v2 pith:W42K5J6D submitted 2020-08-20 math.AC math.COmath.RA

Sergey Fomin , Lauren Williams , Andrei Zelevinsky This is my paper · ORCID
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This is a preliminary draft of Chapter 6 of our forthcoming textbook "Introduction to Cluster Algebras." Chapters 1-3 have been posted as arXiv:1608.05735. Chapters 4-5 have been posted as arXiv:1707.07190. This installment contains: Chapter 6. Cluster structures in commutative rings

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Cited by 3 Pith papers

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

  1. Cluster structures on $SL_n/SO_n$

    math.RT 2026-07 conditional novelty 7.0 of 10

    SL_n/SO_n, its strata ˚S_w, and the symmetric matrices Sym_n admit cluster algebra structures, obtained by folding the cluster structure on SL_n.

  2. Electrical networks, Grassmannians, and cluster algebras

    math.CO 2026-07 accept novelty 7.0 of 10

    For odd n the circular-minor cluster algebra CM_n is isomorphic to the Grassmannian cluster algebra A_{n-1,2n} after freezing/trivializing n central variables, relating circular total positivity to Grassmannian positi...

  3. Upper cluster structure on Kac--Moody Richardson varieties

    math.RT 2025-06 conditional novelty 7.0 of 10

    Open Richardson varieties in symmetrizable Kac-Moody flag varieties, including twisted-product cases, are shown to carry upper cluster algebra coordinate rings.

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