Pimsner algebras and Gysin sequences from principal circle actions

Francesca Arici, Jens Kaad, Giovanni Landi

Research output: Contribution to journalJournal articleResearchpeer-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 languageEnglish
JournalJournal of Noncommutative Geometry
Volume10
Issue number1
Pages (from-to)29-64
ISSN1661-6952
DOIs
Publication statusPublished - 2016
Externally publishedYes

Keywords

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

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