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Open AccessArticle

The Invariant Two-Parameter Function of Algebras ψ

1
Dpto. de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, Calle Tarfia s/n, 41012 Sevilla, Spain
2
Dpto. de Física Aplicada III, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Camino de los Descubrimientos, 41092 Sevilla, Spain
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Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(4), 89; https://doi.org/10.3390/mca24040089
Received: 12 September 2019 / Revised: 10 October 2019 / Accepted: 11 October 2019 / Published: 14 October 2019
(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications)
At present, the research on invariant functions for algebras is very extended since Hrivnák and Novotný defined in 2007 the invariant functions ψ and φ as a tool to study the Inönü–Wigner contractions (IW-contractions), previously introduced by those authors in 1953. In this paper, we introduce a new invariant two-parameter function of algebras, which we call ψ ¯ , as a tool which makes easier the computations and allows researchers to deal with contractions of algebras. Our study of this new function is mainly focused in Malcev algebras of the type Lie, although it can also be used with any other types of algebras. The main goal of the paper is to prove, by means of this function, that the five-dimensional classical-mechanical model built upon certain types of five-dimensional Lie algebras cannot be obtained as a limit process of a quantum-mechanical model based on a fifth Heisenberg algebra. As an example of other applications of the new function obtained, its computation in the case of the Lie algebra induced by the Lorentz group S O ( 3 , 1 ) is shown and some open physical problems related to contractions are also formulated. View Full-Text
Keywords: invariant functions; contractions of algebras; Lie algebras; Malcev algebras; Heisenberg algebras invariant functions; contractions of algebras; Lie algebras; Malcev algebras; Heisenberg algebras
MDPI and ACS Style

Escobar, J.M.; Núñez-Valdés, J.; Pérez-Fernández, P. The Invariant Two-Parameter Function of Algebras ψ. Math. Comput. Appl. 2019, 24, 89.

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