2000/02/15 by Alain Connes, Connes, Alain, Henri Moscovici +1 · 2 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA
paper · pdf · doi:10.48550/arxiv.math/0002125
35 pages
arxiv created 2000/02/15 · openalex publication_date 2000/02/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Cyclic cohomology has been recently adapted to the treatment of Hopf symmetry in noncommutative geometry. The resulting theory of characteristic classes for Hopf algebras and their actions on algebras allows to expand the range of applications of cyclic cohomology. It is the goal of the present paper to illustrate these recent developments, with special emphasis on the application to transverse index theory, and point towards future directions. In particular, we highlight the remarkable accord between our framework for cyclic cohomology of Hopf algebras on one hand and both the algebraic as well as the analytic theory of quantum groups on the other, manifest in the construction of the modular square.