1999/05/03 by Alain Connes, Connes, Alain, Henri Moscovici +1
Mathematics · #16W30 #18G60 #19D55 #46L80 #58B30 #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA #msc:16W30 #msc:18G60 #msc:19D55 #msc:46L80 #msc:58B30
paper · pdf · doi:10.48550/arxiv.math/9905013
To appear in Letters in Mathematical Physics 48 (1)
arxiv created 1999/05/03 · arxiv updated 2009/11/30
We associate canonically a cyclic module to any Hopf algebra endowed with a modular pair, consisting of a group-like element and a character, in involution. This provides the key construct allowing to extend cyclic cohomology to Hopf algebras in the non-unimodular case and further to develop a theory of characteristic classes for actions of Hopf algebras compatible not only with traces but also with the modular theory of weights. It applies to ribbon and to coribbon algebras, as well as to quantum groups and their duals.