Smooth algebras associated to Smale spaces and extensions by Schatten ideals

Dimitrios Gerontogiannis (University of Glasgow)

Thursday 11th March 16:00-17:00 Please contact the organizers for Zoom coordinates

Abstract

In the 1980's, Douglas initiated the study of smooth extensions of C*-algebras; C*-algebraic extensions by the ideal of compact operators that on certain dense *-subalgebras reduce to algebraic extensions by Schatten ideals. Douglas studied smooth extensions of C(X), for X being a finite complex. Shortly after, Douglas and Voiculescu studied the case of odd sphere extensions. In the noncommutative setting, examples of C*-algebras with a pervading presence of smooth extensions include the Cuntz-Krieger algebras (Goffeng-Mesland) and crossed product C*-algebras formed by Gromov hyperbolic groups acting on their boundary (Emerson-Nica). In this talk I will present the notion of smoothness of C*-algebras and that smooth extensions of Ruelle algebras (higher dimensional analogues of Cuntz-Krieger algebras) associated to Smale spaces are generic, in some sense. The degree of smoothness of extensions in the case of Ruelle algebras has interesting connections with the Hausdorff dimension of the underlying Smale space. This research is part of my PhD thesis.

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