Generating Higher-Order Lie Algebras by Expanding Maurer Cartan Forms

Abstract

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.

References in corpus (4)

• Expanding Lie (super)algebras through abelian semigroups
• Expansions of algebras and superalgebras and some applications
• Dual Formulation of the Lie Algebra S-expansion Procedure
• S-Expansion of Higher-Order Lie Algebras

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