2006/10/20 by Igor Nikonov, I. Nikonov, Nikonov, I. +2
Mathematics · #16E40 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #math.KT #math.QA #msc:16E40
paper · pdf · doi:10.48550/arxiv.math/0610615
An revised and extended version of talk, given by the second author at the "Noncommutative Geometry and Cyclic Homology", Newton Institute, August 2006
arxiv created 2006/10/20 · openalex publication_date 2006/10/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with the theory of cup-products in Hopf-type cyclic cohomology of algebras and coalgebras. Here we give detailed proofs of the statements, announced in our previous paper. We show that the cyclic cohomology of a coalgebra can be obtained from a construction involving noncommutative Weil algebra. Then we use a generalization of Quillen and Crainic's construction to define the cup-product. We discuss the relation of the introduced cup-product and S-operations on cyclic cohomology. After this we describe the relation of this type of product and bivariant cyclic cohomology. In the last section we briefly discuss the relation of our constructions with that of Khalkhali and Rangipour.