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Cyclic Cohomology and Hopf Algebras

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Abstract

We associate canonically a cyclic module to any Hopf algebra endowed with a modular pair in involution, consisting of a group-like element and a character. This provides the key construction for allowing the extension of cyclic cohomology to Hopf algebras in the nonunimodular case and, further, to developing a theory of characteristic classes for actions of Hopf algebras compatible not only with traces but also with the modular theory of weights. This applies to both ribbon and coribbon algebras as well as to quantum groups and their duals.

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Authors and Affiliations

  1. College de France, 3 rue d'Ulm, 75005, Paris, France

    Alain Connes

  2. Department of Mathematics, The Ohio State University, 231 W 18th Avenue, Columbus, OH, 43210, U.S.A

    Henri Moscovici

Authors
  1. Alain Connes
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  2. Henri Moscovici
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Connes, A., Moscovici, H. Cyclic Cohomology and Hopf Algebras. Letters in Mathematical Physics 48, 97–108 (1999). https://doi.org/10.1023/A:1007527510226

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  • DOI: https://doi.org/10.1023/A:1007527510226

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