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...
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| Format: | Article |
| Language: | en_US |
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Scuola normale superiore di Pisa
2017
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| Online Access: | http://hdl.handle.net/1721.1/107196 https://orcid.org/0000-0002-0710-1416 |
| _version_ | 1826208936302215168 |
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| author | Andruskiewitsch, Nicolas Cuadra, Juan Etingof, Pavel I |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Andruskiewitsch, Nicolas Cuadra, Juan Etingof, Pavel I |
| author_sort | Andruskiewitsch, Nicolas |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T14:14:39Z |
| format | Article |
| id | mit-1721.1/107196 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:14:39Z |
| publishDate | 2017 |
| publisher | Scuola normale superiore di Pisa |
| record_format | dspace |
| spelling | mit-1721.1/1071962022-09-28T19:29:27Z ON TWO FINITENESS CONDITIONS FOR HOPF ALGEBRAS WITH NONZERO INTEGRAL Andruskiewitsch, Nicolas Cuadra, Juan Etingof, Pavel I Massachusetts Institute of Technology. Department of Mathematics Etingof, Pavel I 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. National Science Foundation (U.S.) (Grant DMS-1000113) 2017-03-06T18:57:39Z 2017-03-06T18:57:39Z 2015-06 2012-06 Article http://purl.org/eprint/type/JournalArticle 0391-173X http://hdl.handle.net/1721.1/107196 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. https://orcid.org/0000-0002-0710-1416 en_US http://dx.doi.org/10.2422/2036-2145.201206_011 Annali della Scuola normale superiore di Pisa, Classe di scienze Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Scuola normale superiore di Pisa arXiv |
| spellingShingle | Andruskiewitsch, Nicolas Cuadra, Juan Etingof, Pavel I ON TWO FINITENESS CONDITIONS FOR HOPF ALGEBRAS WITH NONZERO INTEGRAL |
| title | ON TWO FINITENESS CONDITIONS FOR HOPF ALGEBRAS WITH NONZERO INTEGRAL |
| title_full | ON TWO FINITENESS CONDITIONS FOR HOPF ALGEBRAS WITH NONZERO INTEGRAL |
| title_fullStr | ON TWO FINITENESS CONDITIONS FOR HOPF ALGEBRAS WITH NONZERO INTEGRAL |
| title_full_unstemmed | ON TWO FINITENESS CONDITIONS FOR HOPF ALGEBRAS WITH NONZERO INTEGRAL |
| title_short | ON TWO FINITENESS CONDITIONS FOR HOPF ALGEBRAS WITH NONZERO INTEGRAL |
| title_sort | on two finiteness conditions for hopf algebras with nonzero integral |
| url | http://hdl.handle.net/1721.1/107196 https://orcid.org/0000-0002-0710-1416 |
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