Special Session 109: Cluster Algebras, Hall Algebras and Their Applications

Fundamental relations in quantum cluster algebras
Xueqing Chen
University of Wisconsin-Whitewater
USA
Co-Author(s):    Junyuan Huang, Ming Ding, Fan Xu
Abstract:
Let A_q be an arbitrary quantum cluster algebra with principal coefficients. We give the fundamental relations between the quantum cluster variables arising from one-step mutations from the initial cluster in A_q. Immediately and directly, we obtain an algebra homomorphism from the corresponding (untwisted) quantum group to A_q. This is a joint work with J. Huang, M. Ding and F. Xu.