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


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.


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Leonardo Castellani. "Lie Derivatives along Antisymmetric Tensors, and the M-Theory Superalgebra." J. Phys. Math. 3 1 - 7, March 2011.


Published: March 2011
First available in Project Euclid: 29 January 2013

zbMATH: 1264.83041
Digital Object Identifier: 10.4303/jpm/P110504

Primary: 53Z05 , 83F05

Keywords: cosmology , Differential geometry , Relativity and gravitational theory

Rights: Copyright © 2011 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.3 • March 2011
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