ON TWO FINITENESS CONDITIONS FOR HOPF ALGEBRAS WITH NONZERO INTEGRAL
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 conject...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Scuola normale superiore di Pisa
2017
|
| Online Access: | http://hdl.handle.net/1721.1/107196 https://orcid.org/0000-0002-0710-1416 |
| Summary: | 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 Dăscălescu 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. |
|---|