## Journal of Physical Mathematics

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

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

#### 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

**Permanent link to this document**

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

**Keywords**

Differential geometry Relativity and gravitational theory 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