Linear Representations and Frobenius Morphisms of Groupoids
Given a morphism of (small) groupoids with an injective object map, we provide sufficient and necessary conditions under which the induction and co-induction functors between the categories of linear representations are naturally isomorphic. A morphism with this property is termed a Frobenius morphi...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210056 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Linear Representations and Frobenius Morphisms of Groupoids / J.J. Barbarán Sánchez, L. El Kaoutit // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 31 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-210056 |
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Barbarán Sánchez, J.J. El Kaoutit, L. 2025-12-02T09:30:23Z 2019 Linear Representations and Frobenius Morphisms of Groupoids / J.J. Barbarán Sánchez, L. El Kaoutit // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 31 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 18B40, 20L05, 20L99; 18D10,16D90, 18D35 arXiv: 1806.09327 https://nasplib.isofts.kiev.ua/handle/123456789/210056 https://doi.org/10.3842/SIGMA.2019.019 Given a morphism of (small) groupoids with an injective object map, we provide sufficient and necessary conditions under which the induction and co-induction functors between the categories of linear representations are naturally isomorphic. A morphism with this property is termed a Frobenius morphism of groupoids. As a consequence, an extension by a subgroupoid is Frobenius if and only if each fibre of the (left or right) pull-back biset has finitely many orbits. Our results extend and clarify the classical Frobenius reciprocity formulae in the theory of finite groups, and characterize Frobenius extensions of algebras with enough orthogonal idempotents. Research supported by the Spanish Ministerio de Econom´ıa y Competitividad and the European Union FEDER, grant MTM2016-77033-P. The authors would like to thank the referees for their comments and suggestions, which helped us to improve the earlier version of this paper. We are also grateful to Paolo Saracco for his careful reading and for his comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Linear Representations and Frobenius Morphisms of Groupoids Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Linear Representations and Frobenius Morphisms of Groupoids |
| spellingShingle |
Linear Representations and Frobenius Morphisms of Groupoids Barbarán Sánchez, J.J. El Kaoutit, L. |
| title_short |
Linear Representations and Frobenius Morphisms of Groupoids |
| title_full |
Linear Representations and Frobenius Morphisms of Groupoids |
| title_fullStr |
Linear Representations and Frobenius Morphisms of Groupoids |
| title_full_unstemmed |
Linear Representations and Frobenius Morphisms of Groupoids |
| title_sort |
linear representations and frobenius morphisms of groupoids |
| author |
Barbarán Sánchez, J.J. El Kaoutit, L. |
| author_facet |
Barbarán Sánchez, J.J. El Kaoutit, L. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Given a morphism of (small) groupoids with an injective object map, we provide sufficient and necessary conditions under which the induction and co-induction functors between the categories of linear representations are naturally isomorphic. A morphism with this property is termed a Frobenius morphism of groupoids. As a consequence, an extension by a subgroupoid is Frobenius if and only if each fibre of the (left or right) pull-back biset has finitely many orbits. Our results extend and clarify the classical Frobenius reciprocity formulae in the theory of finite groups, and characterize Frobenius extensions of algebras with enough orthogonal idempotents.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210056 |
| citation_txt |
Linear Representations and Frobenius Morphisms of Groupoids / J.J. Barbarán Sánchez, L. El Kaoutit // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 31 назв. — англ. |
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AT barbaransanchezjj linearrepresentationsandfrobeniusmorphismsofgroupoids AT elkaoutitl linearrepresentationsandfrobeniusmorphismsofgroupoids |
| first_indexed |
2025-12-07T21:24:13Z |
| last_indexed |
2025-12-07T21:24:13Z |
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1850886222969307136 |