2022/05/31 by Ivan Bartulović, Bartulović, Ivan
Mathematics · #18M15 #2020 Mathematics Subject Classification. 16T05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2205.15641
openalex publication_date 2022/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1998, Connes and Moscovici defined the cyclic cohomology of Hopf algebras. In 2010, Khalkhali and Pourkia proposed a braided generalization: to any Hopf algebra H in a braided category \mathcal B, they associate a paracocyclic object in \mathcal B. In this paper we explicitly compute the powers of the paracocyclic operator of this paracocyclic object. Also, we introduce twisted modular pairs in involution for H and derive (co)cyclic modules from them. Finally, we relate the paracocyclic object associated with H to that associated with an H-module coalgebra via a categorical version of the Connes-Moscovici trace.