@misc{10481/58913,
year = {2019},
month = {10},
url = {http://hdl.handle.net/10481/58913},
abstract = {At present, the research on invariant functions for algebras is very extended since Hrivnák
and Novotný defined in 2007 the invariant functions y and j 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 ¯y, 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 SO(3, 1) is shown and some open physical problems related to contractions are
also formulated.},
organization = {This research was funded by the Spanish Ministerio de Ciencia e Innovación and Junta de Andalucía via
grants No. MTM2013-40455-P and No. FQM-326 (J.N.-V.) and No. FQM-160 (P.P.-F.).},
publisher = {MDPI},
keywords = {Invariant functions},
keywords = {Contractions of algebras},
keywords = {Lie algebras},
keywords = {Malcev algebras},
keywords = {Heisenberg algebras},
title = {The Invariant Two-Parameter Function of Algebras ψ},
doi = {10.3390/mca24040089},
author = {Escobar, José María and Núñez-Valdés, Juan and Pérez Fernández, Pedro},
}