Pimsner algebras and Gysin sequences from principal circle actions

Francesca Arici; Jens Kaad; Giovanni Landi

doi:10.4171/JNCG/228

Pimsner algebras and Gysin sequences from principal circle actions

Francesca Arici, Jens Kaad, Giovanni Landi

University of Trieste

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

A self Morita equivalence over an algebra B, given by a B-bimodule E, is thought of as a line bundle over B. The corresponding Pimsner algebra O _E is then the total space algebra of a non-commutative principal circle bundle over B. A natural Gysin-like sequence relates the KK-theories of O _E and of B. Interesting examples come from O _E a quantum lens space over B a quantum weighted projective line (with arbitrary weights). The KK-theory of these spaces is explicitly computed and natural generators are exhibited.

Original language	English
Journal	Journal of Noncommutative Geometry
Volume	10
Issue number	1
Pages (from-to)	29-64
ISSN	1661-6952
DOIs	https://doi.org/10.4171/JNCG/228
Publication status	Published - 2016
Externally published	Yes

Keywords

Circle actions
Gysin sequences
KK-theory
Pimsner algebras
Quantum lens spaces
Quantum principal bundles
Quantum weighted projective spaces

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title = "Pimsner algebras and Gysin sequences from principal circle actions",

abstract = "A self Morita equivalence over an algebra B, given by a B-bimodule E, is thought of as a line bundle over B. The corresponding Pimsner algebra O E is then the total space algebra of a non-commutative principal circle bundle over B. A natural Gysin-like sequence relates the KK-theories of O E and of B. Interesting examples come from O E a quantum lens space over B a quantum weighted projective line (with arbitrary weights). The KK-theory of these spaces is explicitly computed and natural generators are exhibited.",

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AU - Arici, Francesca

AU - Kaad, Jens

AU - Landi, Giovanni

PY - 2016

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N2 - A self Morita equivalence over an algebra B, given by a B-bimodule E, is thought of as a line bundle over B. The corresponding Pimsner algebra O E is then the total space algebra of a non-commutative principal circle bundle over B. A natural Gysin-like sequence relates the KK-theories of O E and of B. Interesting examples come from O E a quantum lens space over B a quantum weighted projective line (with arbitrary weights). The KK-theory of these spaces is explicitly computed and natural generators are exhibited.

AB - A self Morita equivalence over an algebra B, given by a B-bimodule E, is thought of as a line bundle over B. The corresponding Pimsner algebra O E is then the total space algebra of a non-commutative principal circle bundle over B. A natural Gysin-like sequence relates the KK-theories of O E and of B. Interesting examples come from O E a quantum lens space over B a quantum weighted projective line (with arbitrary weights). The KK-theory of these spaces is explicitly computed and natural generators are exhibited.

KW - Circle actions

KW - Gysin sequences

KW - KK-theory

KW - Pimsner algebras

KW - Quantum lens spaces

KW - Quantum principal bundles

KW - Quantum weighted projective spaces

U2 - 10.4171/JNCG/228

DO - 10.4171/JNCG/228

M3 - Journal article

SN - 1661-6952

VL - 10

SP - 29

EP - 64

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

IS - 1

ER -

Pimsner algebras and Gysin sequences from principal circle actions

Abstract

Keywords

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