dorsal/arxiv
View SchemaIntegrals for braided Hopf algebras
| Authors | Yuri Bespalov, Thomas Kerler, Volodymyr Lyubashenko, Vladimir Turaev |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9709020 |
| URL | https://arxiv.org/abs/q-alg/9709020 |
| Journal | J. Pure Appl. Algebra 148 (2000), no. 2, 113-164 |
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.
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"abstract": "Let H be a Hopf algebra in a rigid braided monoidal category with split\nidempotents. We prove the existence of integrals on (in) H characterized by the\nuniversal property, employing results about Hopf modules, and show that their\ncommon target (source) object Int H is invertible. The fully braided version of\nRadford\u0027s formula for the fourth power of the antipode is obtained. Connections\nof integration with cross-product and transmutation are studied. The results\napply to topological Hopf algebras, e.g. a torus with a hole, which do not have\nadditive structure.",
"arxiv_id": "q-alg/9709020",
"authors": [
"Yuri Bespalov",
"Thomas Kerler",
"Volodymyr Lyubashenko",
"Vladimir Turaev"
],
"categories": [
"q-alg",
"math.QA"
],
"journal_ref": "J. Pure Appl. Algebra 148 (2000), no. 2, 113-164",
"title": "Integrals for braided Hopf algebras",
"url": "https://arxiv.org/abs/q-alg/9709020"
},
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