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Tracing cyclic homology pairings under twisting of graded algebras

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Abstract

We give a description of cyclic cohomology and its pairing with K-groups for 2-cocycle deformation of algebras graded over discrete groups. The proof relies on a realization of monodromy for the Gauss–Manin connection on periodic cyclic cohomology in terms of the cup product action of group cohomology.

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Acknowledgements

The authors would like to thank Wolfgang Lück and Ryszard Nest for fruitful comments. They also thank the following programs/Grants for their support which enabled collaboration for this paper: Simons - Foundation Grant 346300 and the Polish Government MNiSW 2015–2019 matching fund; The Isaac Newton Institute for Mathematical Sciences for the programme Operator algebras: subfactors and their applications. This work was supported by: EPSRC Grant Number EP/K032208/1 and DFG (SFB 878). M.Y. thanks the operator algebra group at University of Münster for their hospitality during his stay, and Yasu Kawahigashi for financial support (JSPS KAKENHI Grant Number 15H02056).

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  1. Makoto Yamashita

    Present address: Department of Mathematics, University of Oslo, Oslo, Norway

Authors and Affiliations

  1. Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, 48149, Münster, Germany

    Sayan Chakraborty

  2. Department of Mathematics, Ochanomizu University, Otsuka 2-1-1, Bunkyo, Tokyo, Japan

    Makoto Yamashita

  3. Stat-Math unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata, 700108, India

    Sayan Chakraborty

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  1. Sayan Chakraborty
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Chakraborty, S., Yamashita, M. Tracing cyclic homology pairings under twisting of graded algebras. Lett Math Phys 109, 1625–1664 (2019). https://doi.org/10.1007/s11005-018-01147-7

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