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A quantum analog of generalized cluster algebras. (English) Zbl 1408.16008
Summary: 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 [A. Berenstein and A. Zelevinsky, Adv. Math. 195, No. 2, 405–455 (2005; Zbl 1124.20028)]. In the case of rank two, we extend some structural results from the classical theory of generalized cluster algebras obtained in [L. Chekhov and M. Shapiro, Int. Math. Res. Not. 2014, No. 10, 2746–2772 (2014; Zbl 1301.30042)] and [D. Rupel, “Greedy bases in rank 2 generalized cluster algebras”, Preprint, arXiv:1309.2567] to the quantum case.

MSC:
16G20 Representations of quivers and partially ordered sets
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
17B35 Universal enveloping (super)algebras
18E30 Derived categories, triangulated categories (MSC2010)
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