Unital embeddings of the Jiang-Su algebra are not unique

Abstract: Classifying embeddings up to approximate unitary equivalence, together with the accompanying existence theorem, is a cornerstone step in the modern approach to classification of C*-algebras. Partly motivated by Gabe's result that any pair of unital embeddings of the Cuntz algebra $\mathcal{O}_{\infty}$ into a unital C*-algebra are approximately unitarily equivalent, Schafhauser, Tikuisis and White asked whether this must also be case for unital embeddings of the Jiang-Su algebra. Despite this being true for a class of sufficiently regular targets by a theorem of Robert, the answer to the question is negative. In this talk, I will present recent work where we produce a counterexample; in particular, one can choose the full free product of two copies of the Jiang-Su algebra as target.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | video )

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Noncommutative geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click meet.google.com/zjd-ehrs-wtx (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.

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