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Operator Algebra and Noncommutative Geometry Seminar Series
July 12, 2018 @ 3:30 pm - 4:30 pm
Suspensions of graphs, and C*-algebras.
The suspension of the 1-sided shift space X associated to a graph E is the quotient of X \times [0,\infty) in which (x, 1) is glued to (\sigma(x), 0). Each positive real number l induces a transformation of SX by translation in the second coordinate. When l = 1, this dynamics encodes the original shift \sigma. Constructing C*-algebras that encode these transformations is difficult because they are not open maps. I’ll describe an approach based on realising the dynamics induced by l in terms of a topological quiver constructed from E, and explain why the result agrees quite well with what we’d might expect from a symbolic-dynamics point of view for rational values of l.