Lecture----数学院晨兴数学中心

Title:	On the automorphism groups of cluster algebras with coefficients
Speaker:	常文 (清华大学)
Time:	2015-1-6, 14:30-16:30
Place:	510
Abstract:	We study the cluster automorphism group of a cluster algebra with geometriccoefficients. For this, we introduce the notion of gluing free cluster algebra, and show that under a weak condition the cluster automorphism group of a gluing free cluster algebra is a subgroup of the cluster automorphism group of its principal part cluster algebra (i.e. the corresponding cluster algebra without coefficients). We show that several classes of cluster algebras with coefficients are gluing free, for example, cluster algebras with principal coefficients, cluster algebras with universal geometric coefficients, and cluster algebras from surfaces (except a 4-gon) with coefficients from boundaries. Moreover, except four kinds of surfaces, the cluster automorphism group of a cluster algebra from a surface with coefficients from boundaries is isomorphic to the cluster automorphism group of its principal part cluster algebra. This is joint work with Bin Zhu.
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