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.
|
PDF
com_ren_mat_361_617-652_2023.pdf - Published Version Download (763kB) | Preview |
Abstract
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 |
Actions (login required)
 |
View Item |
