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Dual Formulation of the Lie Algebra S-expansion Procedure · Around

2009

Dual Formulation of the Lie Algebra S-expansion Procedure

Izaurieta, Fernando, Pérez, Alfredo, Rodríguez, Eduardo et al.

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The expansion of a Lie algebra entails finding a new, bigger algebra G, through a series of well-defined steps, from an original Lie algebra g.

One incarnation of the method, the so-called S-expansion, involves the use of a finite abelian semigroup S to accomplish this task.
In this paper we put forward a dual formulation of the S-expansion method which is based on the dual picture of a Lie algebra given by the Maurer-Cartan forms.
The dual version of the method is useful in finding a generalization to the case of a gauge free differential algebra, which in turn is relevant for physical applications in, e.g., Supergravity.

Built on

D. Sullivan, Infinitesimal Computations in Topology
1977
Earlier work this paper cites.
R. D’Auria, P. Fré, Geometric Supergravity in D = 11 D=11 and its Hidden Supergroup
1982
Earlier work this paper cites.
E. Witten, ( 2 + 1 ) (2+1) -Dimensional Gravity as an Exactly Soluble System
1988
Earlier work this paper cites.
M. Hatsuda, M. Sakaguchi, Wess–Zumino Term for the AdS Superstring and Generalized İnönü–Wigner Contraction
2003
Earlier work this paper cites.

Similar

J. A. de Azcárraga, J. M. Izquierdo, M. Picón, O. Varela, Generating Lie and Gauge Free Differential (Super)Algebras by Expanding Maurer–Cartan Forms and Chern–Simons Supergravity
2003
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M. Nakahara, Geometry, Topology and Physics
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J. A. de Azcárraga, J. M. Izquierdo, M. Picón, O. Varela, Extensions, Expansions, Lie Algebra Cohomology and Enlarged Superspaces
2004
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F. Izaurieta, E. Rodríguez, P. Salgado, Expanding Lie (Super)Algebras through Abelian Semigroups
2006
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Then

E. Rodríguez, Formas de Transgresión y Semigrupos Abelianos en Supergravedad
2006
Later among the works it cites.
J. A. de Azcárraga, J. M. Izquierdo, M. Picón, O. Varela, Expansions of Algebras and Superalgebras and Some Applications
2007
Later among the works it cites.
F. Izaurieta, E. Rodríguez, P. Salgado, Construction of Lie Algebras and Invariant Tensors through Abelian Semigroups
2008
Later among the works it cites.

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