On two finiteness conditions for Hopf algebras with nonzero integral
Quantum Algebra
2013-05-14 v2 Category Theory
Rings and Algebras
Representation Theory
Abstract
A Hopf algebra is co-Frobenius when it has a nonzero integral. It is proved that the composition length of the indecomposable injective comodules over a co-Frobenius Hopf algebra is bounded. As a consequence, the coradical filtration of a co-Frobenius Hopf algebra is finite; this confirms a conjecture by Sorin D\u{a}sc\u{a}lescu and the first author. The proof is of categorical nature and the same result is obtained for Frobenius tensor categories of subexponential growth. A family of co-Frobenius Hopf algebras that are not of finite type over their Hopf socles is constructed, answering so in the negative another question by the same authors.
Keywords
Cite
@article{arxiv.1206.5934,
title = {On two finiteness conditions for Hopf algebras with nonzero integral},
author = {Nicolás Andruskiewitsch and Juan Cuadra and Pavel Etingof},
journal= {arXiv preprint arXiv:1206.5934},
year = {2013}
}
Comments
Minor changes. Final version, to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5); 33 pages