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

2024/04/19 by Abhishek Banerjee, Banerjee, Abhishek, Subhajit Das +3
Mathematics · #16E40 #18D10 #47A53 #58B34 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2404.15162

openalex publication_date 2024/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Fredholm modules over categories, Connes periodicity and classes in cyclic cohomology
• Categorified Fredholm Modules and Chern Characters
• Analytic cyclic cohomology
• Categorified Chern character and cyclic cohomology
• Cyclic Theory and the Bivariant Chern-Connes Character