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Mathematics > Operator Algebras
Title: Hilbert spaces over $C^*$-tensor categories, Fredholm modules and cyclic cohomology
(Submitted on 19 Apr 2024)
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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