Artículo
Abstract:
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.
Registro:
| Documento: | Artículo |
| Título: | Some remarks on representations of Yang-Mills algebras |
| Autor: | Herscovich, E. |
| Filiación: | Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina |
| Año: | 2015 |
| Volumen: | 56 |
| Número: | 1 |
| DOI: | http://dx.doi.org/10.1063/1.4905857 |
| Título revista: | Journal of Mathematical Physics |
| Título revista abreviado: | J. Math. Phys. |
| ISSN: | 00222488 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v56_n1_p_Herscovich |
Referencias:
- Cartan, E., Les groupes de transformations continus, infinis, simples (1909) Ann. Sci. éc. Norm. Super., 26 (3), pp. 93-161
- Connes, A., Dubois-Violette, M., Yang-Mills algebra (2002) Lett. Math. Phys., 61 (2), pp. 149-158
- Geĺfand, I.M., Fuks, D.B., Cohomologies of the Lie algebra of vector fields on the circle (1968) Funkcional. Anal. i Priložen, 2 (4), pp. 92-93
- Herscovich, E., Solotar, A., Representation theory of Yang-Mills algebras (2011) Ann. Math., 173 (2), pp. 1043-1080
- Kac, V.G., (1985) Infinite-Dimensional Lie Algebras, , 2nd ed. (Cambridge University Press, Cambridge)
- Knapp, A.W., (2002) Lie Groups Beyond an Introduction, 140. , Progress in Mathematics 2nd ed. (Birkhäuser Boston, Inc., Boston, MA)
- Kuranishi, M., On everywhere dense imbedding of free groups in Lie groups (1951) Nagoya Math. J., 2, pp. 63-71
- Lu, C.H., Wan, Z.X., On the minimal number of generators of the Lie algebra ?( (1986) J. Algebra, 101 (2), pp. 470-472
- Nekrasov, N.A., Lectures on open strings, and noncommutative gauge theories (2003) Unity From Duality: Gravity, Gauge Theory and Strings (Les Houches, 2001), pp. 477-495. , NATO Advanced Study Institute, EDP Science, Les Ulis
Citas:
---------- APA ----------
(2015) . Some remarks on representations of Yang-Mills algebras. Journal of Mathematical Physics, 56(1).http://dx.doi.org/10.1063/1.4905857
---------- CHICAGO ----------
Herscovich, E. "Some remarks on representations of Yang-Mills algebras" . Journal of Mathematical Physics 56, no. 1 (2015).http://dx.doi.org/10.1063/1.4905857
---------- MLA ----------
Herscovich, E. "Some remarks on representations of Yang-Mills algebras" . Journal of Mathematical Physics, vol. 56, no. 1, 2015.http://dx.doi.org/10.1063/1.4905857
---------- VANCOUVER ----------
Herscovich, E. Some remarks on representations of Yang-Mills algebras. J. Math. Phys. 2015;56(1).http://dx.doi.org/10.1063/1.4905857
