Generating Higher-Order Lie Algebras by Expanding Maurer Cartan Forms

Details Generating Higher-Order Lie Algebras by Expanding Maurer Cartan Forms Generating Higher-Order Lie Algebras by Expanding Maurer Cartan Forms

2010-04-30

arxiv.org/abs/1004.5503v1

Journal of Mathematical Physics 50, 123527 (2009)

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1063/1.3272997

By means of a generalization of the Maurer-Cartan expansion method we construct a procedure to obtain expanded higher-order Lie algebras. The expanded higher order Maurer-Cartan equations for the case $\mathcal{G}=V_{0}\oplus V_{1}$ are found. A dual formulation for the S-expansion multialgebra procedure is also considered. The expanded higher order Maurer Cartan equations are recovered from S-expansion formalism by choosing a special semigroup. This dual method could be useful in finding a generalization to the case of a generalized free differential algebra, which may be relevant for physical applications in, e.g., higher-spin gauge theories.

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