Cyclic Cohomology, Hopf Algebras and the Modular Theory
Quantum Algebra
2007-05-23 v1 Operator Algebras
Abstract
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.
Keywords
Cite
@article{arxiv.math/9905013,
title = {Cyclic Cohomology, Hopf Algebras and the Modular Theory},
author = {Alain Connes and Henri Moscovici},
journal= {arXiv preprint arXiv:math/9905013},
year = {2007}
}
Comments
To appear in Letters in Mathematical Physics 48 (1)