Playa de la Malvarrosa (Sorolla) Mathematical and Theoretical High Energy Physics (fismat/hep-th)
Departamento de Física Teórica
Universidad de Valencia e IFIC (CSIC)



7-9 Marzo 2006

Prof. L. J. Boya


27-30 Marzo 2006

Prof. E.A. Bergshoeff


Mayo 2006

Prof. E. Ivanov


30 Mayo-1 Junio 2006

Prof. I. Bars


14-16 Enero 2008

Prof. P. Salgado


Ene. 22-Feb. 28, 2008

Prof. P.K. Townsend


20-23 Octubre 2008

Prof. J.A. de Azcárraga and Prof. J.M. Figueroa O'Farrill




An introduction to n-ary algebras and their applications


J.A. de Azcárraga¹ and J.M. Figueroa O'Farrill¹ ²,

¹ Department of Theoretical Physics, Valencia University, and IFIC (CSIC-UVEG)

² School of Mathematical Sciences, Edinburgh University



 October 2008, Monday 20 to Thursday 23, 15.30-17.30
Theoretical Physics Department Seminar Room

Bldg. D, 4th floor, room 4426, Facultad de Física, Valencia Univ. Burjassot Campus



Synopsis (tentative):

1. From Lie algebras to n-ary algebras. Higher order generalized Lie algebras (GLA) and n-Lie or Filippov algebras (FA). Examples. The structure of FA algebras. Cohomology and homology for GLA and FA.

2. Study of n-Lie (Filippov) algebras. Basic definitions and main theorems. Examples. Metric Lie and  n-Lie algebras: Basic structure theory. Classification (results).

3. Triple systems. Lie-theoretic construction. Examples. Relation with Lie (super)algebras.

4. Applications to d=3 superconformal field theory. The Bagger Lambert Gustavsson model (N=8 superconformal Chern-Simons). N<8 superconformal Chern-Simons.

5. Higher order Poisson structures: Generalized Poisson and Nambu-Poisson structures. The problem of quantizing Nambu mechanics.

The lectures will be delivered in two-hour sessions with a 10m break. Approximately, parts 1 and 5 will be covered by JA, and parts 2,3,4 by J F O'F.

[Information about the Theor. Phys. Department may be found at ]