A new characterisation of principal actions

DOI10.1006/jfan.2000.3561zbMath0960.46049OpenAlexW2093744203MaRDI QIDQ1568540

David Alexandre Ellwood

Publication date: 27 August 2000

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.2000.3561

zbMATH Keywords

dual coactionbimodule morphismcanonical Hopf algebraindex of transversely elliptic operators on a foliationKac systemprincipal groups actiontransverse frame bundle

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Noncommutative dynamical systems (46L55) Noncommutative geometry (à la Connes) (58B34)

Related Items (26)

An Atiyah sequence for noncommutative principal bundles ⋮ Fixed point algebras for easy quantum groups ⋮ Examples of non-compact quantum group actions ⋮ Noncommutative index theory for mirror quantum spheres ⋮ Compact group actions on topological and noncommutative joins ⋮ Graph \(C^ *\)-algebras and \({\mathbb Z}_ 2\)-quotients of quantum spheres. ⋮ Free actions of compact quantum groups on unital \(C^\ast\)-algebras ⋮ Free actions of compact quantum groups on \(C^*\)-algebras. III. ⋮ The \(K\)-theory of twisted multipullback quantum odd spheres and complex projective spaces ⋮ Equivariant dimensions of graph \(C^\ast\)-algebras ⋮ Fixed points of compact quantum groups actions on Cuntz algebras ⋮ Cyclic-homology Chern-Weil theory for families of principal coactions ⋮ Categorically Morita equivalent compact quantum groups ⋮ Pullbacks and nontriviality of associated noncommutative vector bundles ⋮ Noncommutative Fiber Bundles ⋮ The spatial Rokhlin property for actions of compact quantum groups ⋮ Gauge theory on noncommutative Riemannian principal bundles ⋮ Free actions of compact abelian groups on \(C^{\ast}\)-algebras. I. ⋮ A locally trivial quantum Hopf fibration. ⋮ Exotic Coactions ⋮ Noncommutative Borsuk-Ulam-type conjectures revisited ⋮ Free actions on C*-algebra suspensions and joins by finite cyclic groups ⋮ Invariants in noncommutative dynamics ⋮ Lifting spectral triples to noncommutative principal bundles ⋮ Model theory and Rokhlin dimension for compact quantum group actions ⋮ The geometry of quantum lens spaces: real spectral triples and bundle structure

Cites Work

• Hopf algebras, renormalization and noncommutative geometry
• Hopf algebras, cyclic cohomology and the transverse index theorem
• The local index formula in noncommutative geometry
• Unitaires multiplicatifs et dualité pour les produits croisés de $\mathrm{C}^*$-algèbres
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