ON TWO FINITENESS CONDITIONS FOR HOPF ALGEBRAS WITH NONZERO INTEGRAL
Author(s)Andruskiewitsch, Nicolas; Cuadra, Juan; Etingof, Pavel I
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Annali della Scuola normale superiore di Pisa, Classe di scienze
Scuola normale superiore di Pisa
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.
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