SIGMA 9 (2013), 051, 15 pages      arXiv:1111.6328      https://doi.org/10.3842/SIGMA.2013.051

Twisted Cyclic Cohomology and Modular Fredholm Modules

Adam Rennie ^a, Andrzej Sitarz ^{b, c} and Makoto Yamashita ^d
a) School of Mathematics and Applied Statistics, University of Wollongong, Wollongong NSW 2522, Australia
^b) Institute of Mathematics of the Polish Academy of Sciences, ul. Sniadeckich 8, Warszawa, 00-950 Poland
^c) Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland
^d) Department of Mathematics, Ochanomizu University, Otsuka 2-1-1, Tokyo, Japan

Received January 24, 2013, in final form July 22, 2013; Published online July 30, 2013

Abstract
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 SU_q(2).

Key words: twisted cyclic cohomology; spectral triple; modular theory; KMS weight.

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