2019/04/16 by Bernt Tore Jensen, Jensen, Bernt Tore, Alastair J. King +3
Chemistry · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Molecular spectroscopy and chirality #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1904.07849
openalex publication_date 2019/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In \citeJKS we gave an (additive) categorification of Grassmannian cluster algebras, using the category \CM(A) of Cohen-Macaulay modules for a certain Gorenstein order A. In this paper, using a cluster tilting object in the same category \CM(A), we construct a compatible pair (B, L), which is the data needed to define a quantum cluster algebra. We show that when (B, L) is defined from a cluster tilting object with rank 1 summands, this quantum cluster algebra is (generically) isomorphic to the corresponding quantum Grassmannian.