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Journals
Axioms
Special Issues
New Perspectives in Lie Algebras
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New Perspectives in Lie Algebras

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Algebra and Number Theory".

Deadline for manuscript submissions: closed (31 August 2025) | Viewed by 3347

Special Issue Editor

Dr. Rutwig Campoamor-Stursberg

E-Mail Website
Guest Editor
Instituto de Matemática Interdisciplinar, Departamento de Geometría y Topología, Universidad Complutense de Madrid, Plaza de Ciencias 3, E-28040 Madrid, Spain
Interests: Lie algebras; mechanics; differential equations; differential geometry; group theoretical methods in physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Lie algebras constitute one of the most versatile tools in modern mathematics, appearing in many different disciplines like Mechanics, Differential Geometry, Differential Equations or Quantum Theories, being also a relevant technique in Control Theory or Robotics, among others.

We invite researchers to contribute either original papers or review articles concerning currently open problems within the theory of Lie algebras/superalgebras, finite or infinite, and/or dealing with its applications in other disciplines, including engineering sciences.

Articles with strong geometrical backgrounds or describing new computational methods in representation or structural theory, as well as in applications, are especially welcome. Beyond the forementioned topics, the Special Issue is also open to receiving further ideas and applications.

Dr. Rutwig Campoamor-Stursberg
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • structure theory of Lie algebras and superalgebras
  • classification problems
  • representation theory
  • realizations by vector fields or differential operators
  • computational methods
  • lie algebras and symmetries of systems
  • applications to other natural sciences

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

55 pages, 1261 KB  
Article
A Java Library to Perform S-Expansions of Lie Algebras
by Carlos Inostroza, Igor Kondrashuk, Nelson Merino and Felip Nadal
Axioms 2025, 14(10), 735; https://doi.org/10.3390/axioms14100735 - 29 Sep 2025
Viewed by 658
Abstract
The contraction method is a procedure that allows to establish non-trivial relations between Lie algebras and has had successful applications in both mathematics and theoretical physics. This work deals with generalizations of the contraction procedure, with a main focus on the so-called S [...] Read more.
The contraction method is a procedure that allows to establish non-trivial relations between Lie algebras and has had successful applications in both mathematics and theoretical physics. This work deals with generalizations of the contraction procedure, with a main focus on the so-called S-expansion method, as it includes most of the other generalized contractions. Basically, the S-expansion combines a Lie algebra G with a finite abelian semigroup S in order to define new S-expanded algebras. After giving a description of the main ingredients used in this paper, we present a Java library that automates the S-expansion procedure. With this computational tool, we are able to represent Lie algebras and semigroups, so we can perform S-expansions of Lie algebras using arbitrary semigroups. We explain how the library methods have been constructed and how they work; then, we give a set of example programs aimed to solve different problems. They are presented so that any user can easily modify them to perform their own calculations, without necessarily being an expert in Java. Finally, some comments about further developments and possible new applications are made. Full article
(This article belongs to the Special Issue New Perspectives in Lie Algebras)
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9 pages, 224 KB  
Article
On Some Unification Theorems: Yang–Baxter Systems; Johnson–Tzitzeica Theorem
by Florin Felix Nichita
Axioms 2025, 14(3), 156; https://doi.org/10.3390/axioms14030156 - 21 Feb 2025
Viewed by 647
Abstract
This paper investigates the properties of the Yang–Baxter equation, which was initially formulated in the field of theoretical physics and statistical mechanics. The equation’s framework is extended through Yang–Baxter systems, aiming to unify algebraic and coalgebraic structures. The unification of the algebra structures [...] Read more.
This paper investigates the properties of the Yang–Baxter equation, which was initially formulated in the field of theoretical physics and statistical mechanics. The equation’s framework is extended through Yang–Baxter systems, aiming to unify algebraic and coalgebraic structures. The unification of the algebra structures and the coalgebra structures leads to an extension for the duality between finite dimensional algebras and finite dimensional coalgebras to the category of finite dimensional Yang–Baxter structures. In the same manner, we attempt to unify the Tzitzeica–Johnson theorem and its dual version, obtaining a new theorem about circle configurations. Full article
(This article belongs to the Special Issue New Perspectives in Lie Algebras)
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11 pages, 248 KB  
Article
An Integrated Integrable Hierarchy Arising from a Broadened Ablowitz–Kaup–Newell–Segur Scenario
by Wen-Xiu Ma
Axioms 2024, 13(8), 563; https://doi.org/10.3390/axioms13080563 - 19 Aug 2024
Cited by 16 | Viewed by 1225
Abstract
This study introduces a 4×4 matrix eigenvalue problem and develops an integrable hierarchy with a bi-Hamiltonian structure. Integrability is ensured by the zero-curvature condition, while the Hamiltonian structure is supported by the trace identity. Explicit derivations yield second-order and third-order integrable [...] Read more.
This study introduces a 4×4 matrix eigenvalue problem and develops an integrable hierarchy with a bi-Hamiltonian structure. Integrability is ensured by the zero-curvature condition, while the Hamiltonian structure is supported by the trace identity. Explicit derivations yield second-order and third-order integrable equations, illustrating the integrable hierarchy. Full article
(This article belongs to the Special Issue New Perspectives in Lie Algebras)
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