On finite GK-dimensional Nichols algebras of diagonal type
This paper contributes to the proof of the conjecture posed in [5], stating that a Nichols algebra of diagonal type with finite Gelfand-Kirillov dimension has a finite (generalized) root system. We prove the conjecture assuming that the rank is 3 or that the braiding is of Cartan type.
| Authors: | ; |
|---|---|
| Format: | Article |
| Publication date: | 2023 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:280967 |
| Online Access: | https://ddd.uab.cat/record/280967 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6722311 |
| Access Level: | Open access |
| Keyword: | Hopf algebras Nichols algebras Gelfand-kirillov dimension |
| _version_ | 1878740545468104704 |
|---|---|
| author | Angiono, Ivan|||0000-0001-8767-1648 |
| author2 | García Iglesias, Agustín |
| author2_role | author |
| author_browse | Angiono, Ivan|||0000-0001-8767-1648 García Iglesias, Agustín |
| author_facet | Angiono, Ivan|||0000-0001-8767-1648 García Iglesias, Agustín |
| author_role | author |
| collection | Dipòsit Digital de Documents de la UAB |
| description | This paper contributes to the proof of the conjecture posed in [5], stating that a Nichols algebra of diagonal type with finite Gelfand-Kirillov dimension has a finite (generalized) root system. We prove the conjecture assuming that the rank is 3 or that the braiding is of Cartan type. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_d4fdde9efe2e6d9b59eb7b45a3a3e103 |
| institution | Universitat Autònoma de Barcelona |
| instname_str | Universitat Autònoma de Barcelona |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:ddd.uab.cat:280967 |
| publishDate | 2023 |
| publishDateSort | 2023 |
| reponame_str | Dipòsit Digital de Documents de la UAB |
| spelling | On finite GK-dimensional Nichols algebras of diagonal type rank 3 and Cartan type Angiono, Ivan|||0000-0001-8767-1648 García Iglesias, Agustín Hopf algebras Nichols algebras Gelfand-kirillov dimension This paper contributes to the proof of the conjecture posed in [5], stating that a Nichols algebra of diagonal type with finite Gelfand-Kirillov dimension has a finite (generalized) root system. We prove the conjecture assuming that the rank is 3 or that the braiding is of Cartan type. https://ddd.uab.cat/record/280967 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6722311 |
| spellingShingle | On finite GK-dimensional Nichols algebras of diagonal type Angiono, Ivan|||0000-0001-8767-1648 Hopf algebras Nichols algebras Gelfand-kirillov dimension |
| title | On finite GK-dimensional Nichols algebras of diagonal type |
| title_full | On finite GK-dimensional Nichols algebras of diagonal type |
| title_fullStr | On finite GK-dimensional Nichols algebras of diagonal type |
| title_full_unstemmed | On finite GK-dimensional Nichols algebras of diagonal type |
| title_short | On finite GK-dimensional Nichols algebras of diagonal type |
| title_sort | On finite GK-dimensional Nichols algebras of diagonal type |
| topic | Hopf algebras Nichols algebras Gelfand-kirillov dimension |
| topic_facet | Hopf algebras Nichols algebras Gelfand-kirillov dimension |
| url | https://ddd.uab.cat/record/280967 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6722311 |