Gysin sequences and SU(2)-symmetries of C*-algebras
Operator Algebras
2021-11-10 v1 K-Theory and Homology
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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Cite
@article{arxiv.2012.11186,
title = {Gysin sequences and SU(2)-symmetries of C*-algebras},
author = {Francesca Arici and Jens Kaad},
journal= {arXiv preprint arXiv:2012.11186},
year = {2021}
}
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45 pages