Hilbert spaces over $C^*$-tensor categories, Fredholm modules and cyclic cohomology

Abhishek Banerjee; Subhajit Das; Surjeet Kour

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arXiv · 2404.15162

Hilbert spaces over $C^*$-tensor categories, Fredholm modules and cyclic cohomology

Abhishek Banerjee·Subhajit Das·Surjeet Kour

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Abstract

We construct Fredholm modules over an algebra taking values in generalized Hilbert spaces over a rigid $C^*$-tensor category. Using methods of Connes, we obtain Chern characters taking values in cyclic cohomology. These Chern characters are well behaved with respect to the periodicity operator, and depend only on the homotopy class of the Fredholm module.

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Abhishek Banerjee, Subhajit Das, Surjeet Kour. 2024-04-19. Hilbert spaces over $C^*$-tensor categories, Fredholm modules and cyclic cohomology. https://arxiv.org/abs/2404.15162

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