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Fredholm modules over categories, Connes periodicity and classes in cyclic cohomology

Balodi, M and Banerjee, A (2023) Fredholm modules over categories, Connes periodicity and classes in cyclic cohomology. In: Comptes Rendus Mathematique, 361 . pp. 617-652.

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Official URL: https://doi.org/10.5802/crmath.429


We replace a ring with a small C-linear category C , seen as a ring with several objects in the sense of Mitchell. We introduce Fredholm modules over this category and construct a Chern character taking values in the cyclic cohomology of C . We show that this categorified Chern character is homotopy invariant and is well-behaved with respect to the periodicity operator in cyclic cohomology. For this, we also obtain a description of cocycles and coboundaries in the cyclic cohomology of C (and more generally, in the Hopf cyclic cohomology of a Hopf-module category) by means of DG-semicategories equipped with a trace on endomorphism spaces.

Item Type: Journal Article
Publication: Comptes Rendus Mathematique
Publisher: Academie des sciences
Additional Information: The copyright for this article belongs to the Authors.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 19 May 2023 09:46
Last Modified: 19 May 2023 09:46
URI: https://eprints.iisc.ac.in/id/eprint/81567

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