The Brauer-Picard group of the representation category of finite supergroup algebras
We develop further the techniques presented in a previous article (M. Mombelli. Abh. Math. Semin. Univ. Hamb. 82 (2012), 173–192), to study bimodule categories over the representation categories of arbitrary finite-dimensional Hopf algebras. We compute the Brauer-Picard group of equivalence classes of exact invertible bimodule categories over the representation categories of a certain large family of pointed non-semisimple Hopf algebras, the so called supergroup algebras (N. Andruskiewitsch, P. Etingof and S. Gelaki. Michigan Math. J. 49 (2001), 277–298). To obtain this result we first give a classification of equivalence classes of exact indecomposable bimodule categories over such Hopf algebras.
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2014
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| Subjects: | Brauer-Picard group, Tensor category, Module category, |
| Online Access: | http://hdl.handle.net/11086/19337 |
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dig-unc-ar-11086-193372022-10-13T11:07:19Z The Brauer-Picard group of the representation category of finite supergroup algebras Mombelli, Juan Martín Brauer-Picard group Tensor category Module category We develop further the techniques presented in a previous article (M. Mombelli. Abh. Math. Semin. Univ. Hamb. 82 (2012), 173–192), to study bimodule categories over the representation categories of arbitrary finite-dimensional Hopf algebras. We compute the Brauer-Picard group of equivalence classes of exact invertible bimodule categories over the representation categories of a certain large family of pointed non-semisimple Hopf algebras, the so called supergroup algebras (N. Andruskiewitsch, P. Etingof and S. Gelaki. Michigan Math. J. 49 (2001), 277–298). To obtain this result we first give a classification of equivalence classes of exact indecomposable bimodule categories over such Hopf algebras. publishedVersion Fil: Mombelli, Juan Martín. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Fil: Mombelli, Juan Martín. Universidad de Hamburgo. Facultad de Matemáticas, Informática y Ciencias Naturales. Departamento de Matemáticas; Alemania. Matemática Pura 2021-08-06T14:45:45Z 2021-08-06T14:45:45Z 2014 article Mombelli, J. M. (2014). The Brauer-Picard group of the representation category of finite supergroup algebras. Revista de la Unión Matemática Argentina, 55 (1), 83-117. http://hdl.handle.net/11086/19337 http://hdl.handle.net/11086/19337 eng Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ Impreso; Electrónico y/o Digital ISSN 1669-9637 DOI: https://doi.org/10.33044/revuma |
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Argentina |
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Biblioteca 'Ing. Agrónomo Moisés Farber' de la Facultad de Ciencias Agropecuarias |
| language |
eng |
| topic |
Brauer-Picard group Tensor category Module category Brauer-Picard group Tensor category Module category |
| spellingShingle |
Brauer-Picard group Tensor category Module category Brauer-Picard group Tensor category Module category Mombelli, Juan Martín The Brauer-Picard group of the representation category of finite supergroup algebras |
| description |
We develop further the techniques presented in a previous article (M. Mombelli. Abh. Math. Semin. Univ. Hamb. 82 (2012), 173–192), to study bimodule categories over the representation categories of arbitrary finite-dimensional Hopf algebras. We compute the Brauer-Picard group of equivalence classes of exact invertible bimodule categories over the representation categories of a certain large family of pointed non-semisimple Hopf algebras, the so called supergroup algebras (N. Andruskiewitsch, P. Etingof and S. Gelaki. Michigan Math. J. 49 (2001), 277–298). To obtain this result we first give a classification of equivalence classes of exact indecomposable bimodule categories over such Hopf algebras. |
| format |
article |
| topic_facet |
Brauer-Picard group Tensor category Module category |
| author |
Mombelli, Juan Martín |
| author_facet |
Mombelli, Juan Martín |
| author_sort |
Mombelli, Juan Martín |
| title |
The Brauer-Picard group of the representation category of finite supergroup algebras |
| title_short |
The Brauer-Picard group of the representation category of finite supergroup algebras |
| title_full |
The Brauer-Picard group of the representation category of finite supergroup algebras |
| title_fullStr |
The Brauer-Picard group of the representation category of finite supergroup algebras |
| title_full_unstemmed |
The Brauer-Picard group of the representation category of finite supergroup algebras |
| title_sort |
brauer-picard group of the representation category of finite supergroup algebras |
| publishDate |
2014 |
| url |
http://hdl.handle.net/11086/19337 |
| work_keys_str_mv |
AT mombellijuanmartin thebrauerpicardgroupoftherepresentationcategoryoffinitesupergroupalgebras AT mombellijuanmartin brauerpicardgroupoftherepresentationcategoryoffinitesupergroupalgebras |
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1756009587841957888 |