Products in Hopf-cyclic cohomology. (English) Zbl 1147.16011

Kaygun, Atabey

Homology Homotopy Appl. 10, No. 2, 115-133 (2008).

Summary: We construct several pairings in Hopf-cyclic cohomology of (co)module (co)algebras with arbitrary coefficients. As a special case of one of these pairings, we recover the Connes-Moscovici characteristic map in Hopf-cyclic cohomology. We also prove that this particular pairing, along with a few others, would stay the same if we replace the derived category of (co)cyclic modules with the homotopy category of (special) towers of super complexes, or the derived category of mixed complexes.

MSC:

16E40	(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
16W30	Hopf algebras (associative rings and algebras) (MSC2000)

Keywords:

cup products; Hopf-cyclic cohomology; characteristic maps; comodule coalgebras; pairings; derived categories of modules; homotopy categories; mixed complexes