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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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2015
Main Authors: Buchberger, I., Fuchs, J.
Format: Article
Language:English
Published: Інститут математики НАН України 2015
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147008
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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.
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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
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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