SU(2)-symmetries, exact sequences of C*-algebras and subproduct systems

Abstract: Motivated by the study of symmetries of C*-algebras as well as by multivariate operator theory, in this talk we will introduce the notion of an SU(2)-equivariant subproduct system of Hilberts spaces. Through an explicit construction in operator theory, we will obtain Toeplitz and Cuntz-Pimsner algebras, and provide results about their topological invariants.

In particular, we will show that the Toeplitz algebra of the subproduct system of an irreducible SU(2) representation is equivariantly KK-equivalent to the algebra of complex numbers, so that the (K)K-theory groups of the Cuntz-Pimsner algebra can be effectively computed using an exact sequence involving an analogue of the Euler class.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( 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 sju.webex.com/meet/nikolaei (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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