ON TWO FINITENESS CONDITIONS FOR HOPF ALGEBRAS WITH NONZERO INTEGRAL
Name
Etingof_On two finiteness.pdf
Size
335.14 KB
Format
Adobe PDF
Checksum (MD5)
724f4785721674224fab374a218de618
Author(s)
Andruskiewitsch, Nicolas
Cuadra, Juan
Etingof, Pavel I
Date Issued
June 2015
Journal
Annali della Scuola normale superiore di Pisa, Classe di scienze
Publisher
Scuola normale superiore di Pisa
Citation
Andruskiewitsch, Nicolás, Juan Cuadra, and Pavel Etingof. “On Two Finiteness Conditions for Hopf Algebras with Nonzero Integral.” Annali Della Scuola Normale Superiore Di Pisa 2 (2015): 401–440.
Version
Author's final manuscript
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 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
http://dx.doi.org/10.2422/2036-2145.201206_011
