Infinite S-Expansion with Ideal Subtraction and Some Applications

Abstract

According to the literature, the S-expansion procedure involving a finite semigroup is valid no matter what the structure of the original Lie (super)algebra is; However, when something about the structure of the starting (super)algebra is known and when certain particular conditions are met, the S-expansion method (with its features of resonance and reduction) is able not only to lead to several kinds of expanded (super)algebras, but also to reproduce the effects of the standard as well as the generalized Inönü-Wigner contraction. In the present paper, we propose a new prescription for S-expansion, involving an infinite abelian semigroup $S^{(\infty )}$ and the subtraction of an infinite ideal subalgebra. We show that the subtraction of the infinite ideal subalgebra corresponds to a reduction. Our approach is a generalization of the finite S-expansion procedure presented in the literature, and it offers an alternative view of the generalized Inönü-Wigner contraction. We then show how to write the invariant tensors of the target (super)algebras in terms of those of the starting ones in the infinite S-expansion context presented in this work. We also give some interesting examples of application on algebras and superalgebras.

43 pages, title and abstract modified to better represent the content, some sections clarified. Version accepted for publication in Journal of Mathematical Physics

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• Three-dimensional exotic Newtonian supergravity theory with cosmological constant
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Three-dimensional non-relativistic supergravity and torsion
• Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
• Non-relativistic gravity theories in four spacetime dimensions
• A free Lie algebra approach to curvature corrections to flat space-time
• On a Java library to perform S-expansions of Lie algebras
• A Java library to perform S-expansions of Lie algebras
• Boson-fermion algebraic mapping in second quantization