Noncommutative join construction

Speaker(s)

Piotr Mieczysław Hajac

Affiliation

PAN

Date

May 29, 2007, noon

Room

room 5870

Seminar

Seminar Algebraic Topology

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The aim of this talk is to show how to carry out the join construction of compact quantum groups avoiding braiding and replacing the unit interval by an arbitrary unital C*-algebra (noncommutative compact Hausdorff space). This is done in terms of equivariantly projective Hopf-Galois extensions of C*-algebras. The completion of the extended algebra is a natural candidate for a non-crossed product example of a principal extension of C*-algebras in the sense of Ellwood (non-trivial noncommutative principal bundle). The main point is a general and explicit formula for a strong connection, which puts us directly into the framework of the index pairing between K-theory and K-homology. (Based on a joint work with L. Dąbrowski and T. Hadfield.) Piotr M. Hajac (Instytut Matematyczny, Polska Akademia Nauk / Katedra Metod Matematycznych Fizyki, Uniwersytet Warszawski). Joint Noncommutative Geometry and Algebraic Topology Seminar.

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