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arXiv · 1508.00591

On cluster C*-algebras

Igor Nikolaev
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Abstract

We introduce a C*-algebra A(x,Q) attached to the cluster x and a quiver Q. If Q(T) is the quiver coming from a triangulation T of the Riemann surface S with a finite number of cusps, we prove that the primitive spectrum of A(x,Q(T)) times R is homeomorphic to a generic subset of the Teichmueller 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,Q(T)).

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Igor Nikolaev. 2016-05-18. On cluster C*-algebras. https://doi.org/10.1155/2016%2F9639875

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