2002/07/14 by Masoud Khalkhali, M. Khalkhali, Khalkhali, M. +3
Mathematics · #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) #math.KT #math.QA
paper · pdf · doi:10.48550/arxiv.math/0207118
Minor typos corrected. Final version to appear in K-theory
openalex publication_date 2002/07/14 · arxiv created 2003/02/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define a noncommutative analogue of invariant de Rham cohomology. More precisely, for a triple (A,H,M) consisting of a Hopf algebra H, an H-comodule algebra A, an H-module M, and a compatible grouplike element σ in H, we define the cyclic module of invariant chains on A with coefficients in M and call its cyclic homology the invariant cyclic homology of A with coefficients in M. We also develop a dual theory for coalgebras. Examples include cyclic cohomology of Hopf algebras defined by Connes-Moscovici and its dual theory. We establish various results and computations including one for the quantum group SL(q,2).