Integrals for braided Hopf algebras
q-alg
2008-02-03 v2 Quantum Algebra
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.
Keywords
Cite
@article{arxiv.q-alg/9709020,
title = {Integrals for braided Hopf algebras},
author = {Yuri Bespalov and Thomas Kerler and Volodymyr Lyubashenko and Vladimir Turaev},
journal= {arXiv preprint arXiv:q-alg/9709020},
year = {2008}
}
Comments
55 pages, Latex2e with AMSLatex