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SUMMARY:Bundles of C*-algebras around the Effros-Shen algebras - Jack  Spi
 elberg (Arizona State University)
DTSTART:20250718T150500Z
DTEND:20250718T154500Z
UID:TALK233140@talks.cam.ac.uk
DESCRIPTION:For an irrational number t in the unit interval\, the Effros-S
 hen 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 f
 rom the simple continued fraction expansion of t. It is known that these a
 lgebras 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 a
 n appropriate sense\, does give a continuous bundle over [0\,1]. We will a
 lso compare this situation with the Boca-Mundici algebra\, which gives an 
 upper semicontinuous bundle\, but with a different choice of fiber at rati
 onal numbers.
LOCATION:External
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