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Yang-Baxter Equations, Nonassociative Structures and Applications—In Memoriam, Stefan Papadima
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Yang-Baxter Equations, Nonassociative Structures and Applications—In Memoriam, Stefan Papadima

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

Deadline for manuscript submissions: 30 June 2024 | Viewed by 4523

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; Jordan algebras; non-associative structures; topology; differential geometry
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The Yang-Baxter equation first appeared in a paper by the Nobel laureate C.N. Yang and in R.J. Baxter's work. In 1990, at the International Mathematics Congress, three of the four field’s medalists were awarded prizes for their work related to the Yang–Baxter equation. This equation plays a crucial role in many areas of mathematics, physics and computer science. Many scientists have used the axioms of various algebraic structures or computer calculations in order to produce solutions for it, but the full classification of its solutions remains an open problem.

This Special Issue is dedicated to Ștefan Papadima (1953--2018), whom we would like to commemorate as a professor and researcher. I remember our discussions on Artin groups, Yang–Baxter equations and the Alexander polynomial of knots, but there were also other investigations which remained unpublished. We will focus on various aspects of the Yang–Baxter equations, nonassociative structures and the related structures, and we would like to gather together both interesting reviews and research papers.

Dr. Florin 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

  • Artin groups
  • Yang-Baxter equations
  • Alexander polynomial
  • braid groups
  • knot invariants
  • quantum groups
  • cohomology

Published Papers (5 papers)

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Research

15 pages, 336 KiB  
Article
Terracini Loci, Linear Projections, and the Maximal Defect
by Edoardo Ballico
Axioms 2024, 13(4), 271; https://doi.org/10.3390/axioms13040271 - 18 Apr 2024
Viewed by 211
Abstract
We continue the study of Terracini loci formed by x points of a variety embedded in a projective space. Our main results are a refined study of Terracini loci arising from linear projections, the description of the maximal x with a non-empty Terracini [...] Read more.
We continue the study of Terracini loci formed by x points of a variety embedded in a projective space. Our main results are a refined study of Terracini loci arising from linear projections, the description of the maximal x with a non-empty Terracini locus for Hirzebruch surfaces, and the maximal “weight”, “corank”, or “defect” in several cases. For low x, we even show which defects can occur. Full article
(This article belongs to the Special Issue Yang-Baxter Equations, Nonassociative Structures and Applications—In Memoriam, Stefan Papadima)
11 pages, 280 KiB  
Article
Product States of Infinite Tensor Product of JC-algebras
by Fatmah B. Jamjoom and Fadwa M. Algamdei
Axioms 2024, 13(3), 205; https://doi.org/10.3390/axioms13030205 - 18 Mar 2024
Viewed by 594
Abstract
The objective of our study is to generalize the results on product states of the tensor product of two JC-algebras to infinite tensor product JC-algebras. Also, we characterize the tracial product state of the tensor product of two JC-algebras, and the tracial product [...] Read more.
The objective of our study is to generalize the results on product states of the tensor product of two JC-algebras to infinite tensor product JC-algebras. Also, we characterize the tracial product state of the tensor product of two JC-algebras, and the tracial product state of infinite tensor products of JC-algebras. Full article
(This article belongs to the Special Issue Yang-Baxter Equations, Nonassociative Structures and Applications—In Memoriam, Stefan Papadima)
13 pages, 306 KiB  
Article
Minimal and Primitive Terracini Loci of a Four-Dimensional Projective Space
by Edoardo Ballico
Axioms 2024, 13(1), 50; https://doi.org/10.3390/axioms13010050 - 14 Jan 2024
Viewed by 773
Abstract
We study two quite different types of Terracini loci for the order d-Veronese embedding of an n-dimensional projective space: the minimal one and the primitive one (defined in this paper). The main result is that if n=4, [...] Read more.
We study two quite different types of Terracini loci for the order d-Veronese embedding of an n-dimensional projective space: the minimal one and the primitive one (defined in this paper). The main result is that if n=4, d≥19 and x≤2d, no subset with x points is a minimal Terracini set. We give examples that show that the result is sharp. We raise several open questions. Full article
(This article belongs to the Special Issue Yang-Baxter Equations, Nonassociative Structures and Applications—In Memoriam, Stefan Papadima)
7 pages, 264 KiB  
Communication
Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems
by Florin F. Nichita
Axioms 2023, 12(4), 341; https://doi.org/10.3390/axioms12040341 - 31 Mar 2023
Cited by 1 | Viewed by 834
Abstract
This paper continues a series of papers on unification constructions. After a short discussion on the Euler’s relation, we introduce a matrix version of the Euler’s relation, E I π+U=O. We refer to a related equation, [...] Read more.
This paper continues a series of papers on unification constructions. After a short discussion on the Euler’s relation, we introduce a matrix version of the Euler’s relation, E I π+U=O. We refer to a related equation, the Yang–Baxter equation, and to Yang–Baxter systems. The most consistent part of the paper is on the unification of rings and Boolean algebras. These new structures are related to the Yang–Baxter equation and to Yang–Baxter systems. Full article
(This article belongs to the Special Issue Yang-Baxter Equations, Nonassociative Structures and Applications—In Memoriam, Stefan Papadima)
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16 pages, 335 KiB  
Article
Permutation Groups Generated by γ-Cycles
by Răzvan Diaconescu
Axioms 2022, 11(10), 528; https://doi.org/10.3390/axioms11100528 - 02 Oct 2022
Viewed by 1274
Abstract
A γ-cycle is a cycle of the form (i+1,i+2,…,i+m) in the symmetric group Sn. We study the subgroups of Sn generated by several sets of [...] Read more.
A γ-cycle is a cycle of the form (i+1,i+2,…,i+m) in the symmetric group Sn. We study the subgroups of Sn generated by several sets of γ-cycles. Our mathematical development is strongly supported by computational experiments and proofs based on do-it-yourself programming with the logic-based language Maude. Full article
(This article belongs to the Special Issue Yang-Baxter Equations, Nonassociative Structures and Applications—In Memoriam, Stefan Papadima)
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