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Axioms
Special Issues
Non-associative Structures, Yang–Baxter Equations and Related Topics
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Non-associative Structures, Yang–Baxter Equations and Related Topics

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 May 2021) | Viewed by 9527

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 algebra is receiving more and more attention these days (as a revived research direction). There are two important classes of non-associative structures (Lie structures and Jordan structures), and the attempts to unify (non-)associative structures have led to new, interesting results.

The Yang–Baxter equation first appeared in theoretical physics in a paper by the Nobel laureate C.N. Yang (in 1968) and in statistical mechanics in R.J. Baxter's work (1971). It turned out that this equation plays a crucial role in quantum groups, knot theory, braided categories, analysis of integrable systems, quantum mechanics, non-commutative descent theory, quantum computing, non-commutative geometry, etc.

Contributions related to non-associative algebra and/or to Yang–Baxter equations, solutions to open problems proposed in our previous Special Issues, and related research are warmly invited for consideration for this Special Issue.

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 equations
  • non-associative structure
  • Jordan algebra
  • Hopf algebra
  • associative algebra
  • Lie (co)algebras
  • braces
  • applications and open problems

Published Papers (5 papers)

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Research

21 pages, 342 KiB  
Article
Torsion for Homological Complexes of Nonassociative Algebras with Metagroup Relations
by Sergey Victor Ludkowski
Axioms 2021, 10(4), 319; https://doi.org/10.3390/axioms10040319 - 25 Nov 2021
Cited by 5 | Viewed by 1472
Abstract
The article is devoted to homological complexes and modules over nonassociative algebras with metagroup relations. Smashed tensor products of them are studied. Their torsions and homomorphisms are investigated. Full article
(This article belongs to the Special Issue Non-associative Structures, Yang–Baxter Equations and Related Topics)
10 pages, 272 KiB  
Article
On the Colored and the Set-Theoretical Yang–Baxter Equations
by Laszlo Barna Iantovics and Florin Felix Nichita
Axioms 2021, 10(3), 146; https://doi.org/10.3390/axioms10030146 - 02 Jul 2021
Cited by 4 | Viewed by 1604
Abstract
This paper is related to several articles published in AXIOMS, SCI, etc. The main concepts of the current paper are the colored Yang–Baxter equation and the set-theoretical Yang–Baxter equation. The Euler formula, colagebra structures, and means play an important role in our study. [...] Read more.
This paper is related to several articles published in AXIOMS, SCI, etc. The main concepts of the current paper are the colored Yang–Baxter equation and the set-theoretical Yang–Baxter equation. The Euler formula, colagebra structures, and means play an important role in our study. We show that some new solutions for a certain system of equations lead to colored Yang–Baxter operators, which are related to an Euler formula for matrices, and the set-theoretical solutions to the Yang–Baxter equation are related to means. A new coalgebra is obtained and studied. Full article
(This article belongs to the Special Issue Non-associative Structures, Yang–Baxter Equations and Related Topics)
8 pages, 254 KiB  
Article
Unification Theories: Means and Generalized Euler Formulas
by Radu Iordanescu, Florin Felix Nichita and Ovidiu Pasarescu
Axioms 2020, 9(4), 144; https://doi.org/10.3390/axioms9040144 - 20 Dec 2020
Cited by 5 | Viewed by 2001
Abstract
The main concepts in this paper are the means and Euler type formulas; the generalized mean which incorporates the harmonic mean, the geometric mean, the arithmetic mean, and the quadratic mean can be further generalized. Results on the Euler’s formula, the (modified) Yang–Baxter [...] Read more.
The main concepts in this paper are the means and Euler type formulas; the generalized mean which incorporates the harmonic mean, the geometric mean, the arithmetic mean, and the quadratic mean can be further generalized. Results on the Euler’s formula, the (modified) Yang–Baxter equation, coalgebra structures, and non-associative structures are also included in the current paper. Full article
(This article belongs to the Special Issue Non-associative Structures, Yang–Baxter Equations and Related Topics)
5 pages, 445 KiB  
Article
Some Inequalities for Convex Sets
by George Tsintsifas
Axioms 2020, 9(3), 111; https://doi.org/10.3390/axioms9030111 - 17 Sep 2020
Viewed by 1821
Abstract
The paper concerns inequalities between fundamental quantities as area, perimeter, diameter and width for convex plane fugures. Full article
(This article belongs to the Special Issue Non-associative Structures, Yang–Baxter Equations and Related Topics)
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6 pages, 216 KiB  
Article
On the Product Rule for the Hyperbolic Scator Algebra
by Jan L. Cieśliński and Artur Kobus
Axioms 2020, 9(2), 55; https://doi.org/10.3390/axioms9020055 - 19 May 2020
Cited by 5 | Viewed by 1786
Abstract
Scator set, introduced by Fernández-Guasti and Zaldívar, is endowed with a very peculiar non-distributive product. In this paper we consider the scator space of dimension 1 + 2 and the so called fundamental embedding which maps the subset of scators with non-zero scalar [...] Read more.
Scator set, introduced by Fernández-Guasti and Zaldívar, is endowed with a very peculiar non-distributive product. In this paper we consider the scator space of dimension 1 + 2 and the so called fundamental embedding which maps the subset of scators with non-zero scalar component into 4-dimensional space endowed with a natural distributive product. The original definition of the scator product is induced in a straightforward way. Moreover, we propose an extension of the scator product on the whole scator space, including all scators with vanishing scalar component. Full article
(This article belongs to the Special Issue Non-associative Structures, Yang–Baxter Equations and Related Topics)
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