Cyclic Cohomology, Hopf Algebras and the Modular Theory

Details Cyclic Cohomology, Hopf Algebras and the Modular Theory Cyclic Cohomology, Hopf Algebras and the Modular Theory

1999-05-03

arxiv.org/abs/math/9905013v1

Mathematics

Quantum Algebra

To appear in Letters in Mathematical Physics 48 (1)

Scientific paper

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.

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