Article
Mathematics
Francesco Catino, Marzia Mazzotta, Paola Stefanelli
Summary: The paper aims to provide set-theoretical solutions of the Yang-Baxter equation, including new idempotent ones, by drawing on both classical theory of inverse semigroups and recently studied braces. It introduces a new structure, the inverse semi-brace, to offer new constructions allowing for obtaining new solutions of the Yang-Baxter equation.
JOURNAL OF ALGEBRA
(2021)
Article
Mathematics, Applied
Haijun Cao, Fang Xiao
Summary: The main aim of this study is to characterize affine weak k-algebra H with regular nilpotent structure. As preparation, we investigate some properties of weak Hopf algebra morphisms and prove the adjunction between the category C of weak Hopf algebras whose weak antipodes are anti-algebra morphisms. Then, we prove the main result of this study: the bijective correspondence between the category of affine algebraic k-regular monoids and the category of finitely generated commutative reduced weak k-Hopf algebras.
Article
Mathematics, Applied
F. Cedo, E. Jespers, J. Okninski
Summary: Left braces, introduced by Rump, have been shown to be an important tool in studying set-theoretic solutions of the quantum Yang-Baxter equation, allowing for the construction of new families of solutions. The main result of the paper demonstrates that every finite abelian group is a subgroup of the additive group of a finite simple left brace with metabelian multiplicative group with abelian Sylow subgroups. This complements the authors' earlier unexpected results on a abundance of finite simple left braces.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2021)
Article
Mathematics
Baojun Li, Yan Wu, Lue Gong
Summary: In this article, we investigate the subgroup properties of certain groups and provide new criteria for the supersolubility or p-nilpotency of a group.
Article
Mathematics, Applied
A. Ballester-bolinches, R. Esteban-Romero, V. Perez-calabuig
Summary: We demonstrate that there are 1,515,429 isomorphism classes of left braces of order 64 with an additive group isomorphic to C4 x C4 x C4.
MATHEMATICS OF COMPUTATION
(2023)
Article
Multidisciplinary Sciences
Vinothkumar Latchoumanane, Murugan Varadhan
Summary: This paper discusses the antimagicness of the rooted product and corona product of graphs. It proves that under certain conditions, the rooted product and corona product of graphs can have antimagic labeling.
Article
Mathematics
Yanpeng Wang, Binzhou Xia, Sanming Zhou
Summary: This paper investigates the regular sets in graph theory and proves some conclusions about regular sets.
DISCRETE MATHEMATICS
(2022)
Article
Mathematics, Applied
Mingzhi Wu, Tiexin Guo, Long Long
Summary: This article introduces the basic concepts and properties of regular L-0(F)-modules, and proves the fundamental theorem of affine geometry in regular L-0(F)-modules based on this.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Marek Lassak
Summary: The Banach-Mazur distance between the parallelogram and the affine-regular hexagon is shown to be 3/2, leading to the conclusion that the diameter of the family of centrally-symmetric planar convex bodies is also 3/2. This fact, along with similar distances between the parallelogram and other affine-regular polygons, has not been formally proven but has been mentioned in related research.
RESULTS IN MATHEMATICS
(2021)
Article
Mathematics, Applied
Xin Nie, Andrea Seppi
Summary: In this study, we generalize the notion of domains of dependence in the Minkowski space and define and study regular domains in the affine space with respect to a proper convex cone. In three dimensions, we prove that every proper regular domain can be uniquely foliated by specific surfaces with constant affine Gaussian curvature. This result is based on the analysis of a Monge-Ampere equation with extended real-valued lower semicontinuous boundary condition.
Article
Physics, Fluids & Plasmas
Miloslav Torda, John Y. Goulermas, Vitaliy Kurlin, Graeme M. Day
Summary: The study focuses on the dense packings of regular convex polygons and their applications in physical and biological systems, as well as discrete and computational geometry. By restricting the configuration space, the authors formulate the problem as a nonlinear constrained optimization problem and solve it using the Entropic Trust Region Packing Algorithm. The study examines the densest packings of various polygons in all 17 plane groups and proposes conjectures about the common symmetries of the densest plane group packings.
Article
Mathematics
Ilya Gorshkov, Timur Nasybullov
Summary: In this short note, it is shown that if a minimal finite skew brace A has a solvable additive group and a non-solvable multiplicative group, then the multiplicative group of A is not simple. Furthermore, the conjecture of A. Smoktunowicz and L. Vendramin is proven to be correct when the order of A is not divisible by 3.
JOURNAL OF ALGEBRA
(2021)
Article
Mathematics, Applied
Adolfo Ballester-Bolinches, Ramon Esteban-Romero, Vicent Perez-Calabuig
Summary: We demonstrate that the number of isomorphism classes of left braces of order 64 with an additive group isomorphic to C(2)xC(2)xC(4)xC(4) is 10,326,821. This concludes the classification of left braces of order 64, which are found to fall into 15,095,601 isomorphism classes.
RICERCHE DI MATEMATICA
(2023)
Article
Computer Science, Theory & Methods
Oliver Roche-Newton, Audie Warren
Summary: This article explores how the structure of the affine group can be used to deduce new incidence theorems and applications in sum-product type problems. By connecting with collinear quadruples, better energy bounds are obtained compared to previous studies. The motivation for this research stems from potential applications to sum-product problems.
DISCRETE & COMPUTATIONAL GEOMETRY
(2021)
Article
Multidisciplinary Sciences
Junjie Jia, Si Chen, Tianyue Shang
Summary: With the rapid development of the Internet and social networks, traditional personalized recommendation systems are no longer effective for group users. To improve the fairness of group recommendations, algorithms based on subgroup divisions can be used, utilizing consensus preferences among users.
ADVANCED THEORY AND SIMULATIONS
(2022)
Article
Mathematics
Francesco Catino, Marzia Mazzotta, Paola Stefanelli
Summary: The paper aims to provide set-theoretical solutions of the Yang-Baxter equation, including new idempotent ones, by drawing on both classical theory of inverse semigroups and recently studied braces. It introduces a new structure, the inverse semi-brace, to offer new constructions allowing for obtaining new solutions of the Yang-Baxter equation.
JOURNAL OF ALGEBRA
(2021)
Article
Mathematics, Applied
Ilaria Colazzo, Arne Van Antwerpen
Summary: This paper investigates left semi-trusses and their interactions with algebraic structures, proving that in the finite case the additive structure is a completely regular semigroup. It also explores the application of almost left semi-braces, showing that set-theoretic solutions of the Yang-Baxter equation arise from this correspondence.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2021)
Article
Mathematics, Applied
Francesco Catino, Ilaria Colazzo, Paola Stefanelli
Summary: This paper introduces a construction technique called strong semilattice of solutions for set-theoretic solutions of the Yang-Baxter equation, which allows one to obtain new solutions, in particular non-bijective solutions of finite order. It also explores a generalization of the algebraic structure of semi-braces based on this new construction technique of solutions, as braces, skew braces, and semi-braces are closely linked with solutions.
FORUM MATHEMATICUM
(2021)
Article
Mathematics, Applied
Marco Castelli, Francesco Catino, Paola Stefanelli
Summary: The main aim of this paper is to provide sufficient conditions for left non-degenerate bijective set-theoretic solutions of the Yang-Baxter equation to be non-degenerate. Additionally, it extends previous results on involutive solutions and answers a question posed by Cedo et al. Furthermore, a theory of extensions is developed to construct new families of set-theoretic solutions.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
(2022)
Article
Mathematics, Applied
Marco Castelli, Francesco Catino, Paola Stefanelli
Summary: This study examines a class of indecomposable involutive set-theoretic solutions of the Yang-Baxter equation with specific imprimitivity blocks, using the algebraic structure of left braces and the dynamical extensions of cycle sets. It also investigates one-generator left braces of multipermutation level 2.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Marco Castelli, Marzia Mazzotta, Paola Stefanelli
Summary: This paper aims to deepen the theory of bijective non-degenerate set-theoretic solutions of the Yang-Baxter equation, not necessarily involutive, using q-cycle sets. We primarily focus on the class of finite indecomposable solutions, particularly studying simple solutions. We provide a group-theoretic characterization of these solutions, including their permutation groups, and discuss some unresolved questions.
FORUM MATHEMATICUM
(2022)
Article
Mathematics
Francesco Catino, Marzia Mazzotta, Maria Maddalena Miccoli, Paola Stefanelli
Summary: The study investigates a new algebraic structure known as weak (left) brace which always provides a set-theoretic solution for the Yang-Baxter equation. This structure has specific binary operations and can construct structures similar to skew braces, forming a subclass of inverse semi-braces. Furthermore, any solution associated with a weak brace behaves close to bijectivity in the full transformation semigroup on S x S.
Article
Mathematics
Francesco Catino, Ferran Cedo, Paola Stefanelli
Summary: We introduce left and right series of left semi-braces and define left and right nilpotent left semi-braces. We study the structure of these semi-braces, generalize some results from skew left braces to left semi-braces, and analyze the cases where the set of additive idempotents is an ideal of the left semi-braces. Finally, we introduce the concept of nilpotent left semi-braces and prove that their multiplicative groups are nilpotent.
JOURNAL OF ALGEBRA
(2022)
Article
Mathematics
I. Colazzo, E. Jespers, A. Van Antwerpen, C. Verwimp
Summary: The algebraic structure of YB-semitrusses is investigated, showing the connection between the right non-degeneracy and bijectivity of finite left non-degenerate set-theoretic solutions of the Yang-Baxter equation. It is also demonstrated that some finite left non-degenerate solutions can be reduced to non-degenerate solutions of smaller size.
JOURNAL OF ALGEBRA
(2022)
Article
Mathematics, Applied
Paola Stefanelli
Summary: We introduce semi-affine structures on groups and show their equivalence to semi-braces. Our new description of semi-braces includes the one presented by Rump for braces. By using specific semi-affine structures, we provide examples of bi-skew braces, including some that are not lambda-homomorphic. Finally, we present a method for determining semi-affine structures on the Zappa product of two groups, which allows for obtaining semi-braces that are not matched product of semi-braces.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2023)
Article
Mathematics
Matteo Varbaro, Hongmiao Yu
Summary: In this paper, a liaison theory via quasi-Gorenstein varieties is developed, and it is applied to derive the connectedness property of general quasi-Gorenstein subspace arrangements and the classical topological Lefschetz duality.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Eric J. Hanson, Xinrui You
Summary: In this paper, we demonstrate the use of arcs in computing bases for the Hom-spaces and first extension spaces between bricks over preprojective algebras of type A. We also classify the weak exceptional sequences over these algebras using this description. Furthermore, we explain the connection between our results and a similar combinatorial model for exceptional sequences over hereditary algebras of type A.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Valery Lunts, Spela Spenko, Michel Van den Bergh
Summary: This article provides a brief review of the cohomological Hall algebra and K-theoretical Hall algebra associated with quivers. It shows a homomorphism between them in the case of symmetric quivers. Additionally, the equivalence of categories of graded modules is established.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Luc Guyot, Ihsen Yengui
Summary: In this article, it is discussed that for any integral domain R, if R is a Bezout domain of Krull dimension <= 1, then its localization ring R(X) is also a Bezout domain of Krull dimension <= 1. The generalization of this result is explored in different cases such as valuation domains and lexicographic monomial orders, and an example is given to show that this result does not hold in the irrational case.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Pedro L. del Angel, E. Javier Elizondo, Cristhian Garay, Felipe Zaldivar
Summary: In this paper, we study the Grassmannian space of 2-dimensional isotropic subspaces with a specific form and symmetry, and characterize its irreducible subvarieties using symplectic Coxeter matroids. We also provide a complete characterization of symplectic matroids of rank 2 that can be represented over C.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Ioannis Emmanouil, Ilias Kaperonis
Summary: In this paper, we study the role of K-absolutely pure complexes in the homotopy category and the pure derived category. We prove that K-abspure is the isomorphic closure and investigate the relationship between strongly fp-injective modules and K-absolutely pure complexes. Furthermore, we demonstrate that, under certain conditions, a K-absolutely pure complex of strongly fp-injective modules can be a K(PInj)-preenvelope containing an injective module complex.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Miroslav Ploscica, Friedrich Wehrung
Summary: This study investigates the lattice of principal ideals in Abelian L-groups and presents relevant results. These results have important applications in the representation of distributive lattices and homomorphisms, as well as in solving the MV spectrum problem.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Christian Garcia, Thaisa Tamusiunas
Summary: We present a Galois correspondence for K-beta-rings, where beta is an action of a finite groupoid on a unital ring R. We recover the correspondence given in [11] for finite groupoids acting on commutative rings.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Andrea Lucchini, Dhara Thakkar
Summary: This paper studies the problem of minimum generating set for finite groups. By testing whether subsets of the group can generate the group, the minimum generating set can be determined. It is proved that the number of these tests can be significantly reduced if the chief series of the group is known, and at most |G|13/5 subsets need to be tested. This implies that the minimum generating set problem for finite groups can be solved in polynomial time.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Ulrich Meierfrankenfeld, Chris Parker, Gernot Stroth
Summary: This paper investigates the local and global structural properties of finite groups. By studying certain properties of finite groups, we obtain important conclusions about subgroups and extend previous research.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Shezad Mohamed
Summary: We prove the existence of a version of Weil descent, or Weil restriction, in the category of D-algebras. This result is obtained under a mild assumption on the associated endomorphisms. As a consequence, we establish the existence of the Weil descent functor in the category of difference algebras.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Annalisa Conversano, Nicolas Monod
Summary: This study solves the problem of whether all Lie groups can be represented faithfully on a countable set by reducing it to the case of simple Lie groups. It provides a solution for all solvable Lie groups and Lie groups with a linear Levi component, proving that every amenable locally compact second countable group acts faithfully on a countable set.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Wesley Fussner, George Metcalfe
Summary: This paper investigates the transfer of algebraic properties between quasivarieties and their relatively finitely subdirectly irreducible members, and establishes equivalences for certain properties under certain conditions. Additionally, the paper studies special cases of quasivarieties and proves decidability for possessing these properties under certain conditions.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Hao Li, Antun Milas
Summary: We analyze the structure of Feigin-Stoyanovsky's principal subspaces of affine Lie algebra and provide novel fermionic character formulas. We show that level one principal subspaces of type A are classically free as vertex algebras.
JOURNAL OF ALGEBRA
(2024)
Article
Mathematics
Raphael Ruimy
Summary: This article investigates the effect of the perverse t-structure in different dimensions and provides concrete examples. In the case of dimensions less than 2, the core of the t-structure is described. For schemes of finite type over a finite field, a best approximation of the perverse t-structure is constructed.
JOURNAL OF ALGEBRA
(2024)
