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

Francesca Arici; Jens Kaad

doi:10.1112/tlm3.12038

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

Francesca Arici^*, Jens Kaad

^*Kontaktforfatter

Institut for Matematik og Datalogi

Leiden University

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

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Abstract

Motivated by the study of symmetries of (Formula presented.) -algebras, as well as by multivariate operator theory, we introduce the notion of an (Formula presented.) -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 (Formula presented.) -theory. In particular, starting from an irreducible representation of (Formula presented.), we show that the corresponding Toeplitz algebra is equivariantly (Formula presented.) -equivalent to the algebra of complex numbers. In this way, we obtain a six-term exact sequence of (Formula presented.) -groups containing a noncommutative analogue of the Euler class.

Originalsprog	Engelsk
Tidsskrift	Transactions of the London Mathematical Society
Vol/bind	8
Udgave nummer	1
Sider (fra-til)	440-492
ISSN	2052-4986
DOI	https://doi.org/10.1112/tlm3.12038
Status	Udgivet - dec. 2021

Bibliografisk note

Funding Information:
This work is part of the research programme VENI with project number 016.192.237, which is (partly) financed by the Dutch Research Council (NWO). JK gratefully acknowledges the financial support from the Independent Research Fund Denmark through grant no. 7014‐00145B and grant no. 9040‐00107B.

Publisher Copyright:
© 2021 The Authors. Transactions of the London Mathematical Society is copyright © London Mathematical Society.

Dokumenter og links

10.1112/tlm3.12038Licens: CC BY-NC-ND

Open Access VersionForlagets udgivne version, 592 KBLicens: CC BY-NC-ND

Citationsformater

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abstract = "Motivated by the study of symmetries of (Formula presented.) -algebras, as well as by multivariate operator theory, we introduce the notion of an (Formula presented.) -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 (Formula presented.) -theory. In particular, starting from an irreducible representation of (Formula presented.), we show that the corresponding Toeplitz algebra is equivariantly (Formula presented.) -equivalent to the algebra of complex numbers. In this way, we obtain a six-term exact sequence of (Formula presented.) -groups containing a noncommutative analogue of the Euler class.",

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note = "Funding Information: This work is part of the research programme VENI with project number 016.192.237, which is (partly) financed by the Dutch Research Council (NWO). JK gratefully acknowledges the financial support from the Independent Research Fund Denmark through grant no. 7014‐00145B and grant no. 9040‐00107B. Publisher Copyright: {\textcopyright} 2021 The Authors. Transactions of the London Mathematical Society is copyright {\textcopyright} London Mathematical Society.",

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N2 - Motivated by the study of symmetries of (Formula presented.) -algebras, as well as by multivariate operator theory, we introduce the notion of an (Formula presented.) -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 (Formula presented.) -theory. In particular, starting from an irreducible representation of (Formula presented.), we show that the corresponding Toeplitz algebra is equivariantly (Formula presented.) -equivalent to the algebra of complex numbers. In this way, we obtain a six-term exact sequence of (Formula presented.) -groups containing a noncommutative analogue of the Euler class.

AB - Motivated by the study of symmetries of (Formula presented.) -algebras, as well as by multivariate operator theory, we introduce the notion of an (Formula presented.) -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 (Formula presented.) -theory. In particular, starting from an irreducible representation of (Formula presented.), we show that the corresponding Toeplitz algebra is equivariantly (Formula presented.) -equivalent to the algebra of complex numbers. In this way, we obtain a six-term exact sequence of (Formula presented.) -groups containing a noncommutative analogue of the Euler class.

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DO - 10.1112/tlm3.12038

M3 - Journal article

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JO - Transactions of the London Mathematical Society

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

Abstract

Bibliografisk note

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