On cluster C∗-algebras

We introduce a c∗-algebra a (x,q) attached to the cluster x and a quiver q. if qt is the quiver coming from triangulation t of the riemann surface s with a finite number of cusps,we prove that the primitive spectrum of a (x,qt) times r is homeomorphic to a generic subset of the teichmüller space of surface s. we conclude with an analog of the tomita-takesaki theory and the connes invariant t (m) for the algebra a (x,qt). © 2016 igor v. nikolaev.