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Journal of Function Spaces
Volume 2016, Article ID 9639875, 8 pages
Research Article

On Cluster -Algebras

Department of Mathematics and Computer Science, St. John’s University, 8000 Utopia Parkway, Queens, New York, NY 11439, USA

Received 4 February 2016; Accepted 18 May 2016

Academic Editor: Gelu Popescu

Copyright © 2016 Igor V. Nikolaev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce a -algebra attached to the cluster and a quiver . If is the quiver coming from triangulation of the Riemann surface with a finite number of cusps, we prove that the primitive spectrum of times is homeomorphic to a generic subset of the Teichmüller space of surface . We conclude with an analog of the Tomita-Takesaki theory and the Connes invariant for the algebra .