Paper-folding models of the CAR algebra

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• Wilhelm Winter (Universität Münster)
• Thursday 17 July 2025, 09:30-10:10
• External.

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TGAW02 - C*-algebras: classification and dynamical constructions

I explain how the CAR algebra admits a Cantor spectrum C-diagonal that is not conjugate to its standard AF diagonal. This is done by classification theory of stably finite nuclear C-algebras, and the diagonal arises by realising the CAR algebra as the crossed product of a free and minimal action on the Cantor space, where the acting group is the product of a locally finite group with the infinite dihedral group. The main ingredient in the construction is a binary subshift associated to the well-known regular paper-folding sequence. The resulting diagonal pair has finite diagonal dimension, and upon taking tensor products one obtains countable many Cantor spectrum diagonals which are pairwise non-conjugate.  This is joint work with Grigoris Kopsacheilis.

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

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