Mathematics – Quantum Algebra
Scientific paper
1997-09-12
J. Pure Appl. Algebra 148 (2000), no. 2, 113-164
Mathematics
Quantum Algebra
55 pages, Latex2e with AMSLatex
Scientific paper
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.
Bespalov Yuri
Kerler Thomas
Lyubashenko Volodymyr
Turaev Vladimir
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