A Quantum Analog of Generalized Cluster Algebras
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We define a quantum analog of a class of generalized cluster algebras which can be viewed as a generalization of quantum cluster algebras defined in Berenstein and Zelevinsky (Adv. Math. 195(2), 405–455 2005). In the case of rank two, we extend some structural results from the classical theory of generalized cluster algebras obtained in Chekhov and Shapiro (Int. Math. Res. Notices 10, 2746–2772 2014) and Rupel (2013) to the quantum case.
KeywordsGeneralized cluster algebra Generalized quantum cluster algebra Laurent phenomenon Standard monomial
Mathematics Subject Classification (2010)Primary 16G20 17B67 Secondary 17B35 18E30
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