Six-term exact sequences for smooth generalized crossed products

Olivier Gabriel; Martin Grensing

doi:10.4171/jncg/124

Six-term exact sequences for smooth generalized crossed products

Olivier Gabriel, Martin Grensing

Institut for Matematiske Fag

4 Citationer (Scopus)

Abstract

We define smooth generalized crossed products and prove six-term exact sequences of Pimsner–Voiculescu type. This sequence may, in particular, be applied to smooth subalgebras of the quantum Heisenberg manifolds in order to compute the generators of their cyclic cohomology. Further, our results include the known results for smooth crossed products. Our proof is based on a combination of arguments from the setting of (Cuntz–)Pimsner algebras and the Toeplitz proof of Bott periodicity.

Originalsprog	Engelsk
Tidsskrift	Journal of Noncommutative Geometry
Vol/bind	7
Udgave nummer	2
Sider (fra-til)	499
Antal sider	25
ISSN	1661-6952
DOI	https://doi.org/10.4171/jncg/124
Status	Udgivet - 2013

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Det Natur- og Biovidenskabelige Fakultet

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10.4171/jncg/124

http://www.ems-ph.org/journals/show_pdf.php?issn=1661-6952&vol=7&iss=2&rank=7

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AU - Gabriel, Olivier

AU - Grensing, Martin

PY - 2013

Y1 - 2013

N2 - We define smooth generalized crossed products and prove six-term exact sequences of Pimsner–Voiculescu type. This sequence may, in particular, be applied to smooth subalgebras of the quantum Heisenberg manifolds in order to compute the generators of their cyclic cohomology. Further, our results include the known results for smooth crossed products. Our proof is based on a combination of arguments from the setting of (Cuntz–)Pimsner algebras and the Toeplitz proof of Bott periodicity.

AB - We define smooth generalized crossed products and prove six-term exact sequences of Pimsner–Voiculescu type. This sequence may, in particular, be applied to smooth subalgebras of the quantum Heisenberg manifolds in order to compute the generators of their cyclic cohomology. Further, our results include the known results for smooth crossed products. Our proof is based on a combination of arguments from the setting of (Cuntz–)Pimsner algebras and the Toeplitz proof of Bott periodicity.

KW - Faculty of Science

KW - K-theory

KW - kk-theory

KW - cyclic cohomology

KW - generalized crossed product

KW - Pimsner algebra

KW - quantum Heisenberg manifolds

U2 - 10.4171/jncg/124

DO - 10.4171/jncg/124

M3 - Journal article

SN - 1661-6952

VL - 7

SP - 499

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

IS - 2

ER -

Six-term exact sequences for smooth generalized crossed products

Abstract

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