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  • Factoriality and class groups of cluster algebras
    Garcia Elsener, Ana ; Lampe, Philipp ; Smertnig, Daniel
    Locally acyclic cluster algebras are Krull domains. Hence their factorization theory is determined by their (divisor) class group and the set of classes containing height-1 prime ideals. Motivated by ... this, we investigate class groups of cluster algebras. We show that any cluster algebra that is a Krull domain has a finitely generated free abelian class group, and that every class contains infinitely many height-1 prime ideals. For a cluster algebra associated to an acyclic seed, we give an explicit description of the class group in terms of the initial exchange matrix. As a corollary, we reprove and extend a classification of factoriality for cluster algebras of Dynkin type. In the acyclic case, we prove the sufficiency of necessary conditions for factoriality given by Geiss-Leclerc-Schröer.
    Source: Advances in mathematics. - ISSN 0001-8708 (Vol. 358, [article no.] 106858, Dec. 2019, 48 str.)
    Type of material - article, component part ; adult, serious
    Publish date - 2019
    Language - english
    COBISS.SI-ID - 172903939

    Link(s):

    https://www.sciencedirect.com/science/article/pii/S0001870819304748
    DOI

source: Advances in mathematics. - ISSN 0001-8708 (Vol. 358, [article no.] 106858, Dec. 2019, 48 str.)
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