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arXiv · 1802.04835

Upper cluster algebras and choice of ground ring

Eric Bucher·John Machacek·Michael Shapiro
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Abstract

We initiate a study of the dependence on the choice of ground ring on the question of whether a cluster algebra is equal to its upper cluster algebra. A condition for when there is equality of the cluster algebra and upper cluster algebra is given by using a variation of Muller's theory of cluster localization. An explicit example exhibiting dependence on the ground ring is provided. We also present a maximal green sequence for this example.

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Eric Bucher, John Machacek, Michael Shapiro. 2018-02-13. Upper cluster algebras and choice of ground ring. https://doi.org/10.1007/s11425-018-9486-6

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