On Cyclic Cohomology of x-Hopf algebras
Mohammad Hassanzadeh

TL;DR
This paper investigates the cyclic cohomology of various x-Hopf algebras, introduces new modules and cocyclic modules, and generalizes the Connes-Moscovici characteristic map for these structures.
Contribution
It computes cyclic cohomology for specific x-Hopf algebras and introduces a pairing that extends the Connes-Moscovici characteristic map to x-Hopf algebras.
Findings
Computed cyclic cohomology for universal enveloping algebras, quantum algebraic tori, and others.
Introduced stable anti Yetter-Drinfeld modules and cocyclic modules for x-Hopf algebras.
Established a pairing that transfers cyclic cocycles between x-Hopf algebras and algebras.
Abstract
In this paper we study the cyclic cohomology of certain x-Hopf algebras: universal enveloping algebras, quantum algebraic tori, the Connes-Moscovici x-Hopf algebroids and the Kadison bialgebroids. Introducing their stable anti Yetter-Drinfeld modules and cocyclic modules, we compute their cyclic cohomology. Furthermore, we provide a pairing for the cyclic cohomology of x-Hopf algebras which generalizes the Connes-Moscovici characteristic map to x-Hopf algebras. This enables us to transfer the x-Hopf algebra cyclic cocycles to algebra cyclic cocycles.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology
