Article
The Invariant Two-Parameter Function of Algebras ψ
Author/s | Escobar, José María
Núñez-Valdés, Juan Pérez Fernández, Pedro |
Department | Universidad de Sevilla. Departamento de Física Aplicada III Universidad de Sevilla. Departamento de Geometría y Topología |
Publication Date | 2019-10 |
Deposit Date | 2020-01-30 |
Published in |
|
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), ... 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. |
Project ID. | MTM2013-40455-P
FQM-326 (J.N.-V.) FQM-160 (P.P.-F.) |
Citation | Escobar, J.M., Núñez-Valdés, J. y Pérez Fernández, P. (2019). The Invariant Two-Parameter Function of Algebras ψ. Mathematical and Computational Applications, 24 (4). Article number 89. |
Files | Size | Format | View | Description |
---|---|---|---|---|
The Invariant Two-Parameter ... | 322.9Kb | [PDF] | View/ | |
This item appears in the following collection(s)
Except where otherwise noted, this item's license is described as: Attribution-NonCommercial-NoDerivatives 4.0 Internacional
Related items
Showing items related by title, author, creator and subject.
-
Article
A computational algebraic geometry approach to enumerate Malcev magma algebras over finite fields
Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan (Wiley, 2016)The set of Mn(K) of n-dimensional Malcev magma algebras over a finite field can be identified with algebraic sets defined ...
-
Article
Algebraic computation of genetic patterns related to three-dimensional evolution algebras
Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan (Elsevier, 2018-02-15)The mitosis process of an eukaryotic cell can be represented by the structure constants of an evolution algebra. Any ...
-
Article
Representation theory of some infinite-dimensional algebras arising in continuously controlled algebra and topology
Muro Jiménez, Fernando (Springer, 2004)In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity ...