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On the Generalized Cluster Algebras of Geometric Type
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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We develop and prove the analogs of some results shown in [Berenstein A., Fomin S., Zelevinsky A., Duke Math. J. 126 (2005), 1–52] concerning lower and upper bounds of cluster algebras to the generalized cluster algebras of geometric type. We show that lower bounds coincide with upper bounds under the conditions of acyclicity and coprimality. Consequently, we obtain the standard monomial bases of these generalized cluster algebras. Moreover, in the appendix, we prove that an acyclic generalized cluster algebra is equal to the corresponding generalized upper cluster algebra without the assumption of the existence of coprimality.
Keywords: cluster algebra, generalized cluster algebra, lower bound, upper bound
Mots-clés : standard monomial. 
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     author = {Liqian Bai and Xueqing Chen and Ming Ding and Fan Xu},
     title = {On the {Generalized} {Cluster} {Algebras} of {Geometric} {Type}},
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}
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Liqian Bai; Xueqing Chen; Ming Ding; Fan Xu. On the Generalized Cluster Algebras of Geometric Type. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a91/

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