Some remarks on representations of Yang-Mills algebras
In this article, we present some new properties of representations of Yang-Mills algebras. We first show that any free Lie algebra with m generators is a quotient of the Yang-Mills algebra ??(n) on n generators, for n ? 2m. We derive from this that any semisimple Lie algebra and even any affine Kac-...
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todo:paper_00222488_v56_n1_p_Herscovich2023-10-03T14:29:50Z Some remarks on representations of Yang-Mills algebras Herscovich, E. In this article, we present some new properties of representations of Yang-Mills algebras. We first show that any free Lie algebra with m generators is a quotient of the Yang-Mills algebra ??(n) on n generators, for n ? 2m. We derive from this that any semisimple Lie algebra and even any affine Kac-Moody algebra is a quotient of ??(n) for n ? 4. Combining this with previous results on representations of Yang-Mills algebras given in [Herscovich and Solotar, Ann. Math. 173(2), 1043-1080 (2011)], one may obtain solutions to the Yang-Mills equations by differential operators acting on sections of twisted vector bundles on the affine space of dimension n ? 4 associated to representations of any semisimple Lie algebra. We also show that this quotient property does not hold for n = 3, since any morphism of Lie algebras from ??(3) to ??(2, k) has in fact solvable image. © 2015 AIP Publishing LLC. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00222488_v56_n1_p_Herscovich |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
In this article, we present some new properties of representations of Yang-Mills algebras. We first show that any free Lie algebra with m generators is a quotient of the Yang-Mills algebra ??(n) on n generators, for n ? 2m. We derive from this that any semisimple Lie algebra and even any affine Kac-Moody algebra is a quotient of ??(n) for n ? 4. Combining this with previous results on representations of Yang-Mills algebras given in [Herscovich and Solotar, Ann. Math. 173(2), 1043-1080 (2011)], one may obtain solutions to the Yang-Mills equations by differential operators acting on sections of twisted vector bundles on the affine space of dimension n ? 4 associated to representations of any semisimple Lie algebra. We also show that this quotient property does not hold for n = 3, since any morphism of Lie algebras from ??(3) to ??(2, k) has in fact solvable image. © 2015 AIP Publishing LLC. |
| format |
JOUR |
| author |
Herscovich, E. |
| spellingShingle |
Herscovich, E. Some remarks on representations of Yang-Mills algebras |
| author_facet |
Herscovich, E. |
| author_sort |
Herscovich, E. |
| title |
Some remarks on representations of Yang-Mills algebras |
| title_short |
Some remarks on representations of Yang-Mills algebras |
| title_full |
Some remarks on representations of Yang-Mills algebras |
| title_fullStr |
Some remarks on representations of Yang-Mills algebras |
| title_full_unstemmed |
Some remarks on representations of Yang-Mills algebras |
| title_sort |
some remarks on representations of yang-mills algebras |
| url |
http://hdl.handle.net/20.500.12110/paper_00222488_v56_n1_p_Herscovich |
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AT herscoviche someremarksonrepresentationsofyangmillsalgebras |
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