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Axioms
Special Issues
Non-associative Structures and Other Related Structures
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Non-associative Structures and Other Related Structures

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

Deadline for manuscript submissions: closed (20 December 2019) | Viewed by 20972

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Dr. Florin Felix Nichita

E-Mail Website
Guest Editor
Simion Stoilow Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania
Interests: (co)algebras; bialgebras; Yang–Baxter equations; Lie (co)algebras; quantum groups; Hopf algebras; duality theories
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Non-associative algebras are currently a fashionable research direction. There are two important classes of non-associative structures: Lie structures and Jordan structures. Various Jordan structures play an important role in quantum group theory and in fundamental physical theories.

In recent years, several attempts to unify non-associative structures have led to interesting results. The UJLA structures are not the only structures which realize such a unification.

Associative algebras and Lie algebras can be unified at the level of Yang–Baxter structures. Several papers published in the open access journal Axioms deal with the Yang–Baxter equation.

The Yang–Baxter equation can be interpreted in terms of logical circuits and, in logic, it represents a kind of compatibility condition when working with many logical sentences in the same time. This equation is also related to the theory of universal quantum gates and to quantum computers. It has many applications in quantum groups and knot theory.

Contributions related to non-associative structures, various aspects of the Yang–Baxter Equation, and their applications are invited.

Dr. Florin Felix Nichita
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

  • Yang–Baxter equation
  • Non-associative algebras
  • Lie structures
  • Jordan structures
  • Associative algebras
  • Unification theories
  • Braces
  • Noncommutative algebras
  • Applications in physics
  • Duality
  • Knot invariants

Published Papers (8 papers)

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Editorial

Jump to: Research

2 pages, 158 KiB  
Editorial
Non-Associative Structures and Other Related Structures
by Florin F. Nichita
Axioms 2020, 9(2), 40; https://doi.org/10.3390/axioms9020040 - 13 Apr 2020
Viewed by 1489
Abstract
In January 2019, MDPI published a book titled Hopf Algebras, Quantum Groups and Yang–Baxter Equations, based on a successful special issue [...] Full article
(This article belongs to the Special Issue Non-associative Structures and Other Related Structures)

Research

Jump to: Editorial

8 pages, 243 KiB  
Article
Separability of Nonassociative Algebras with Metagroup Relations
by Sergey V. Ludkowski
Axioms 2019, 8(4), 139; https://doi.org/10.3390/axioms8040139 - 12 Dec 2019
Cited by 5 | Viewed by 2008
Abstract
This article is devoted to a class of nonassociative algebras with metagroup relations. This class includes, in particular, generalized Cayley–Dickson algebras. The separability of the nonassociative algebras with metagroup relations is investigated. For this purpose the cohomology theory is utilized. Conditions are found [...] Read more.
This article is devoted to a class of nonassociative algebras with metagroup relations. This class includes, in particular, generalized Cayley–Dickson algebras. The separability of the nonassociative algebras with metagroup relations is investigated. For this purpose the cohomology theory is utilized. Conditions are found under which such algebras are separable. Algebras satisfying these conditions are described. Full article
(This article belongs to the Special Issue Non-associative Structures and Other Related Structures)
20 pages, 326 KiB  
Article
Smashed and Twisted Wreath Products of Metagroups
by Sergey V. Ludkowski
Axioms 2019, 8(4), 127; https://doi.org/10.3390/axioms8040127 - 11 Nov 2019
Cited by 9 | Viewed by 1846
Abstract
In this article, nonassociative metagroups are studied. Different types of smashed products and smashed twisted wreath products are scrutinized. Extensions of central metagroups are studied. Full article
(This article belongs to the Special Issue Non-associative Structures and Other Related Structures)
19 pages, 299 KiB  
Article
Branching Functions for Admissible Representations of Affine Lie Algebras and Super-Virasoro Algebras
by Namhee Kwon
Axioms 2019, 8(3), 82; https://doi.org/10.3390/axioms8030082 - 19 Jul 2019
Cited by 1 | Viewed by 2570
Abstract
We explicitly calculate the branching functions arising from the tensor product decompositions between level 2 and principal admissible representations over sl ^ 2 . In addition, investigating the characters of the minimal series representations of super-Virasoro algebras, we present the tensor product decompositions [...] Read more.
We explicitly calculate the branching functions arising from the tensor product decompositions between level 2 and principal admissible representations over sl ^ 2 . In addition, investigating the characters of the minimal series representations of super-Virasoro algebras, we present the tensor product decompositions in terms of the minimal series representations of super-Virasoro algebras for the case of principal admissible weights. Full article
(This article belongs to the Special Issue Non-associative Structures and Other Related Structures)
19 pages, 372 KiB  
Article
Cohomology Theory of Nonassociative Algebras with Metagroup Relations
by Sergey V. Ludkowski
Axioms 2019, 8(3), 78; https://doi.org/10.3390/axioms8030078 - 04 Jul 2019
Cited by 14 | Viewed by 2586
Abstract
Nonassociative algebras with metagroup relations and their modules are studied. Their cohomology theory is scrutinized. Extensions and cleftings of these algebras are studied. Broad families of such algebras and their acyclic complexes are described. For this purpose, different types of products of metagroups [...] Read more.
Nonassociative algebras with metagroup relations and their modules are studied. Their cohomology theory is scrutinized. Extensions and cleftings of these algebras are studied. Broad families of such algebras and their acyclic complexes are described. For this purpose, different types of products of metagroups are investigated. Necessary structural properties of metagroups are studied. Examples are given. It is shown that a class of nonassociative algebras with metagroup relations contains a subclass of generalized Cayley–Dickson algebras. Full article
(This article belongs to the Special Issue Non-associative Structures and Other Related Structures)
11 pages, 268 KiB  
Article
Dual Numbers and Operational Umbral Methods
by Nicolas Behr, Giuseppe Dattoli, Ambra Lattanzi and Silvia Licciardi
Axioms 2019, 8(3), 77; https://doi.org/10.3390/axioms8030077 - 02 Jul 2019
Cited by 4 | Viewed by 4394
Abstract
Dual numbers and their higher-order version are important tools for numerical computations, and in particular for finite difference calculus. Based on the relevant algebraic rules and matrix realizations of dual numbers, we present a novel point of view, embedding dual numbers within a [...] Read more.
Dual numbers and their higher-order version are important tools for numerical computations, and in particular for finite difference calculus. Based on the relevant algebraic rules and matrix realizations of dual numbers, we present a novel point of view, embedding dual numbers within a formalism reminiscent of operational umbral calculus. Full article
(This article belongs to the Special Issue Non-associative Structures and Other Related Structures)
5 pages, 215 KiB  
Article
Unification Theories: New Results and Examples
by Florin F. Nichita
Axioms 2019, 8(2), 60; https://doi.org/10.3390/axioms8020060 - 18 May 2019
Cited by 12 | Viewed by 2513
Abstract
This paper is a continuation of a previous article that appeared in AXIOMS in 2018. A Euler’s formula for hyperbolic functions is considered a consequence of a unifying point of view. Then, the unification of Jordan, Lie, and associative algebras is revisited. We [...] Read more.
This paper is a continuation of a previous article that appeared in AXIOMS in 2018. A Euler’s formula for hyperbolic functions is considered a consequence of a unifying point of view. Then, the unification of Jordan, Lie, and associative algebras is revisited. We also explain that derivations and co-derivations can be unified. Finally, we consider a “modified” Yang–Baxter type equation, which unifies several problems in mathematics. Full article
(This article belongs to the Special Issue Non-associative Structures and Other Related Structures)
5 pages, 224 KiB  
Article
Unification Theories: Examples and Applications
by Florin F. Nichita
Axioms 2018, 7(4), 85; https://doi.org/10.3390/axioms7040085 - 16 Nov 2018
Cited by 8 | Viewed by 2742
Abstract
We consider several unification problems in mathematics. We refer to transcendental numbers. Furthermore, we present some ways to unify the main non-associative algebras (Lie algebras and Jordan algebras) and associative algebras. Full article
(This article belongs to the Special Issue Non-associative Structures and Other Related Structures)
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