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Twisted Cyclic Cohomology and Modular Fredholm Modules
Symmetry, integrability and geometry: methods and applications, Tome 9 (2013) Cet article a éte moissonné depuis la source Math-Net.Ru

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Connes and Cuntz showed in [Comm. Math. Phys. 114 (1988), 515–526] that suitable cyclic cocycles can be represented as Chern characters of finitely summable semifinite Fredholm modules. We show an analogous result in twisted cyclic cohomology using Chern characters of modular Fredholm modules. We present examples of modular Fredholm modules arising from Podleś spheres and from ${\rm SU}_q(2)$.
Keywords: twisted cyclic cohomology; spectral triple; modular theory; KMS weight. 
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Adam Rennie; Andrzej Sitarz; Makoto Yamashita. Twisted Cyclic Cohomology and Modular Fredholm Modules. Symmetry, integrability and geometry: methods and applications, Tome 9 (2013). http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a50/

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