## Journal of Physical Mathematics

### Lie Derivatives along Antisymmetric Tensors, and the M-Theory Superalgebra

Leonardo Castellani

#### Abstract

Free differential algebras (FDAs) provide an algebraic setting for field theories with antisymmetric tensors. The "presentation'' of FDAs generalizes the Cartan-Maurer equations of ordinary Lie algebras, by incorporating $p$-form potentials. An extended Lie derivative along antisymmetric tensor fields can be defined and used to recover a Lie algebra dual to the FDA that encodes all the symmetries of the theory including those gauged by the $p$-forms. The general method is applied to the FDA of $D=11$ supergravity: the resulting dual Lie superalgebra contains the M-theory supersymmetry anticommutators in presence of $2$-branes.

#### Article information

Source
J. Phys. Math., Volume 3 (2011), 1-7.

Dates
First available in Project Euclid: 29 January 2013

https://projecteuclid.org/euclid.jpm/1359468398

Digital Object Identifier
doi:10.4303/jpm/P110504

Zentralblatt MATH identifier
1264.83041

Subjects
Primary: 53Z05: Applications to physics 83F05: Cosmology

#### Citation

Castellani, Leonardo. Lie Derivatives along Antisymmetric Tensors, and the M-Theory Superalgebra. J. Phys. Math. 3 (2011), 1--7. doi:10.4303/jpm/P110504. https://projecteuclid.org/euclid.jpm/1359468398