Bundles of C*-algebras around the Effros-Shen algebras

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• Jack Spielberg (Arizona State University)
• Friday 18 July 2025, 16:05-16:45
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TGAW02 - C*-algebras: classification and dynamical constructions

For an irrational number t in the unit interval, the Effros-Shen algebra (or “continued fraction AF algebra”) is the unique AF algebra with ordered K_0 group (Z+tZ, (Z+tZ)_+), and with [1]_0 = 1. Effros and Shen described the algebra explicitly by constructing a Bratteli diagram from the simple continued fraction expansion of t. It is known that these algebras form a continuous field over (0,1) \ Q. Each rational number has two simple continued fraction expansions, and it is not clear which (if either) is appropriate to use. We will show that their intersection, in an appropriate sense, does give a continuous bundle over [0,1]. We will also compare this situation with the Boca-Mundici algebra, which gives an upper semicontinuous bundle, but with a different choice of fiber at rational numbers.

This talk is part of the Isaac Newton Institute Seminar Series series.

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