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Quantum cluster algebra structures on quantum Grassmannians and their quantum Schubert cells: the finite-type cases

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arxiv 0912.4397 v1 pith:OEAPACIV submitted 2009-12-22 math.QA

Jan E. Grabowski , Stéphane Launois This is my paper · ORCID
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keywords quantumalgebraclusterstructurescasescellsgrassmanniansschubert
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abstract

We exhibit quantum cluster algebra structures on quantum Grassmannians $K_q[Gr(2,n)]$ and their quantum Schubert cells, as well as on $K_q[Gr(3,6)]$, $K_q[Gr(3,7)]$ and $K_q[Gr(3,8)]$. These cases are precisely those where the quantum cluster algebra is of finite type and the structures we describe quantize those found by Scott for the classical situation.

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  1. Abstract Cluster Structures

    math.RA 2025-10 conditional novelty 7.0 of 10

    Cluster algebras, varieties, categories, and surface models all admit "abstract cluster structures," and these structures form a category with finite products, coproducts, and initial and terminal objects.

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