Integrals for braided Hopf algebras

Abstract

Let H be a Hopf algebra in a rigid braided monoidal category with split idempotents. We prove the existence of integrals on (in) H characterized by the universal property, employing results about Hopf modules, and show that their common target (source) object Int H is invertible. The fully braided version of Radford's formula for the fourth power of the antipode is obtained. Connections of integration with cross-product and transmutation are studied. The results apply to topological Hopf algebras, e.g. a torus with a hole, which do not have additive structure.

55 pages, Latex2e with AMSLatex

References in corpus (2)

• Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity
• Genealogy of Nonperturbative Quantum-Invariants of 3-Manifolds: The Surgical Family

Cited by in corpus (1)

• A universal invariant of four-dimensional 2-handlebodies and three-manifolds