Spectral Triples and Generalized Crossed Products

Abstract

We give a construction allowing to lift spectral triples to crossed products by Hilbert bimodules. The spectral triple one obtains is a concrete unbounded representative of the Kasparov product of the spectral triple and the Pimsner-Toeplitz extension associated to the crossed product by the Hilbert bimodule. To prove that the lifted spectral triple is the above-mentioned Kasparov product, we rely on operator-$\ast$-algebras and connexions.

References in corpus (2)

• Contractive spectral triples for crossed products
• Completely Bounded Characterization of Operator Algebras with Involution

Cited by in corpus (6)

• Pimsner algebras and Gysin sequences from principal circle actions
• Shift tail equivalence and an unbounded representative of the Cuntz-Pimsner extension
• A reconstruction theorem for Connes-Landi deformations of commutative spectral triples
• Lifting spectral triples to noncommutative principal bundles
• Pimsner algebras and circle bundles
• Spectral triples on irreversible $C^{\ast }$-dynamical systems