Journal of Physical Mathematics

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

Leonardo Castellani

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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

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

First available in Project Euclid: 29 January 2013

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Digital Object Identifier

Zentralblatt MATH identifier

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

Differential geometry Relativity and gravitational theory Cosmology


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

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