English

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

R2 v1 2026-07-22T19:22:09.977Z