Co-Frobenius Hopf algebras and the coradical filtration
| dc.creator | Andruskiewitsch, Nicolas | |
| dc.creator | Dascalescu, Sorin | |
| dc.date | 2001-02-03 | |
| dc.date.accessioned | 2026-07-07T06:33:25Z | |
| dc.date.available | 2026-07-07T06:33:25Z | |
| dc.description | We prove that a Hopf algebra with a finite coradical filtration is co-Frobenius, i. e. there is a non-zero integral on it. As a consequence, we show that algebras of functions on quantum groups at roots of one are co-Frobenius. We also characterize co-Frobenius Hopf algebras with coradical a Hopf subalgebra. This characterization is in the framework of the lifting method due to H.-J. Schneider and the first-named author. Here is our main result. Let H be a Hopf algebra whose coradical is a Hopf subalgebra. Let gr H be the associated graded Hopf algebra and let R be the diagram of H. Then the following are equivalent: (1) H is co-Frobenius, (2) gr H is co-Frobenius, (3) R is finite dimensional, (4) the coradical filtration of H is finite. This Theorem allows to construct many new examples of co-Frobenius Hopf algebras and opens the way to the classification of ample classes of such Hopf algebras. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0102028 | |
| dc.identifier | http://arxiv.org/abs/math/0102028 | |
| dc.identifier | Math. Z. 243 (2003), no. 1, 145--154. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99187 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16W30 (Primary); 16W35; 17B37 (Secondary) | |
| dc.title | Co-Frobenius Hopf algebras and the coradical filtration | |
| dc.type | text |