CoFrobenius Hopf algebras and the coradical filtration
Abstract
We prove that a Hopf algebra with a finite coradical filtration is coFrobenius, i. e. there is a nonzero integral on it. As a consequence, we show that algebras of functions on quantum groups at roots of one are coFrobenius. We also characterize coFrobenius Hopf algebras with coradical a Hopf subalgebra. This characterization is in the framework of the lifting method due to H.J. Schneider and the firstnamed 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 coFrobenius, (2) gr H is coFrobenius, (3) R is finite dimensional, (4) the coradical filtration of H is finite. This Theorem allows to construct many new examples of coFrobenius Hopf algebras and opens the way to the classification of ample classes of such Hopf algebras.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2001
 arXiv:
 arXiv:math/0102028
 Bibcode:
 2001math......2028A
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Rings and Algebras;
 16W30 (Primary);
 16W35;
 17B37 (Secondary)
 EPrint:
 13 pages