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Continued fractions, directed graphs, and defining spectral triples on Effros-Shen AF algebras (Samantha Brooker, Arizona State University)
Continued fractions, directed graphs, and defining spectral triples on Effros-Shen AF algebras (Samantha Brooker, Arizona State University)
The Effros-Shen algebra corresponding to an irrational number $\theta$ can be described by an inductive sequence of direct sums of matrix algebras, where the continued fraction expansion of $\theta$ encodes the dimensions of the summands, and how the matrix algebras at the nth level fit into the summands at the (n+1)th level. In recent work, […]