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arXiv · 2012.11186

Gysin sequences and SU(2)-symmetries of C*-algebras

Francesca Arici·Jens Kaad
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Abstract

Motivated by the study of symmetries of C*-algebras, as well as by multivariate operator theory, we introduce the notion of an SU(2)-equivariant subproduct system of Hilbert spaces. We analyse the resulting Toeplitz and Cuntz-Pimsner algebras and provide results about their topological invariants through Kasparov's bivariant K-theory. In particular, starting from an irreducible representation of SU(2), we show that the corresponding Toeplitz algebra is equivariantly KK-equivalent to the algebra of complex numbers. In this way, we obtain a six term exact sequence of K-groups containing a noncommutative analogue of the Euler class.

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BibTeXRIS

Francesca Arici, Jens Kaad. 2020-12-21. Gysin sequences and SU(2)-symmetries of C*-algebras. https://doi.org/10.1112/tlm3.12038

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