On the Killing form of Lie Algebras in Symmetric Ribbon Categories
As a step towards the structure theory of Lie algebras in symmetric monoidal categories we establish results involving the Killing form. The proper categorical setting for discussing these issues are symmetric ribbon categories.
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2015 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2015
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147008 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the Killing form of Lie Algebras in Symmetric Ribbon Categories / I. Buchberger, J. Fuchs // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 53 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862707975922122752 |
|---|---|
| author | Buchberger, I. Fuchs, J. |
| author_facet | Buchberger, I. Fuchs, J. |
| citation_txt | On the Killing form of Lie Algebras in Symmetric Ribbon Categories / I. Buchberger, J. Fuchs // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 53 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | As a step towards the structure theory of Lie algebras in symmetric monoidal categories we establish results involving the Killing form. The proper categorical setting for discussing these issues are symmetric ribbon categories.
|
| first_indexed | 2025-12-07T17:08:36Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147008 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:08:36Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Buchberger, I. Fuchs, J. 2019-02-12T18:26:29Z 2019-02-12T18:26:29Z 2015 On the Killing form of Lie Algebras in Symmetric Ribbon Categories / I. Buchberger, J. Fuchs // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 53 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17Bxx; 18D35; 18D10; 18E05 DOI:10.3842/SIGMA.2015.017 https://nasplib.isofts.kiev.ua/handle/123456789/147008 As a step towards the structure theory of Lie algebras in symmetric monoidal categories we establish results involving the Killing form. The proper categorical setting for discussing these issues are symmetric ribbon categories. This paper is a contribution to the Special Issue on New Directions in Lie Theory. The full collection is
 available at http://www.emis.de/journals/SIGMA/LieTheory2014.html.
 We are most grateful to the referees for their valuable comments on an earlier version of this
 note, and in particular for suggesting improvements of the proof of Proposition 3.12. We also thank Christoph Schweigert for discussions and Scott Morrison for bringing Example 2.20(iv) to
 our attention. JF is supported by VR under project no. 621-2013-4207. JF thanks the ErwinSchr¨odinger-Institute
 (ESI) for the hospitality during the programs “Modern Trends in TQFT”
 and “Topological Phases of Quantum Matter” while part of this work was pursued. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Killing form of Lie Algebras in Symmetric Ribbon Categories Article published earlier |
| spellingShingle | On the Killing form of Lie Algebras in Symmetric Ribbon Categories Buchberger, I. Fuchs, J. |
| title | On the Killing form of Lie Algebras in Symmetric Ribbon Categories |
| title_full | On the Killing form of Lie Algebras in Symmetric Ribbon Categories |
| title_fullStr | On the Killing form of Lie Algebras in Symmetric Ribbon Categories |
| title_full_unstemmed | On the Killing form of Lie Algebras in Symmetric Ribbon Categories |
| title_short | On the Killing form of Lie Algebras in Symmetric Ribbon Categories |
| title_sort | on the killing form of lie algebras in symmetric ribbon categories |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147008 |
| work_keys_str_mv | AT buchbergeri onthekillingformofliealgebrasinsymmetricribboncategories AT fuchsj onthekillingformofliealgebrasinsymmetricribboncategories |