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 http://fisteo.uv.es/ ]
