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Cyclic cohomology and Hopf algebras

Alain Connes·Henri Moscovici
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Abstract

We show by a direct computation that, for any Hopf algebra with a modulus-like character, the formulas first introduced in [CM] in the context of characteristic classes for actions of Hopf algebras, do define a cyclic module. This provides a natural generalization of Lie algebra cohomology to the general framework of Noncommutative Geometry, which covers the case of the Hopf algebra associated to n-dimensional transverse geometry [CM] as well as the function algebras of the classical quantum groups.

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Alain Connes, Henri Moscovici. 1999-04-27. Cyclic cohomology and Hopf algebras. https://arxiv.org/abs/math/9904154

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