Article
Mathematics
S. K. Maity, Monika Paul
Summary: This article establishes necessary and sufficient conditions for a topological Clifford semigroup to be a semilattice of topological groups. It shows that certain topological properties are equivalent in a semilattice of topological groups, and proves that the quotient space of a semilattice of topological groups by a full normal Clifford subsemigroup remains a semilattice of topological groups. Additionally, it establishes the topological isomorphism between a family of semilattices of topological groups and their full normal Clifford subsemigroups.
COMMUNICATIONS IN ALGEBRA
(2021)
Article
Mathematics
Mikhailo Dokuchaev, Mykola Khrypchenko, Mayumi Makuta
Summary: This paper defines and studies the concept of a crossed module over an inverse semigroup and its corresponding 4-term exact sequences, known as crossed module extensions. It shows that there is a one-to-one correspondence between equivalence classes of admissible crossed module extensions and elements of the cohomology group H3 <=(T1, A1).
JOURNAL OF ALGEBRA
(2022)
Article
Mathematics, Applied
Iryna Banakh, Taras Banakh, Serhii Bardyla
Summary: A subset A of a semigroup S is called a chain (antichain) if certain conditions are met, and the periodic property applies to every element of S. The property of antichain-finite semigroups can be used to prove the finiteness of a semigroup. An example is presented where an antichain-finite semilattice is not a union of finitely many chains.
Article
Mathematics, Applied
Adel Alahmadi, Hamed Alsulami, S. K. Jain, Efim Zelmanov
Summary: This article reviews various constructions of wreath products of groups, semigroups, Lie algebras, and associative algebras, and discusses their realizations in matrix wreath products of associative algebras. As an application, a new version of Evans's embedding theorem [T. Evans, Embedding theorems for multiplicative systems and projective geometries, Proc. American Math. Soc. 3 (1952) 614-620] is proved.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
(2023)
Article
Mathematics
Taras Banakh, Serhii Bardyla
Summary: The text discusses the concept of closed sets in a class of topological semigroups as well as chain-finite semigroups, proving certain closure conditions and properties of semigroups. The conclusions are complex, involving topological properties of semigroups.
JOURNAL OF ALGEBRA
(2022)
Article
Mathematics
Ilinka Dimitrova, Jorg Koppitz
Summary: In this paper, we study the inverse semigroup IC-n of all partial automorphisms on a finite crown Cn. We consider the elements, determine a generating set of minimal size, and calculate the rank of IC-n.
MONATSHEFTE FUR MATHEMATIK
(2023)
Article
Mathematics, Applied
A. Ballester-Bolinches, V. Perez-Calabuig
Summary: The main objective of this paper is to describe the closure of a finitely generated subgroup of a finitely generated free group in the proabelian topology. Our approach heavily relies on the description of the abelian kernel of a finite inverse semigroup.
RICERCHE DI MATEMATICA
(2023)
Article
Mathematics
John Meakin, David Milan, Zhengpan Wang
Summary: Leavitt inverse semigroups are constructed from directed graphs and closely related to graph inverse semigroups and Leavitt path algebras. A presentation for the Leavitt inverse semigroup of a graph has been found, and the structure of the Leavitt inverse semigroup and its relationship with the Leavitt path algebra have been described.
ADVANCES IN MATHEMATICS
(2021)
Article
Mathematics
V. Manuilov
Summary: The article examines the composition of metrics in metric space and the properties of the inverse semigroup, discussing the definition of C*-algebra and commutativity. It also analyzes the characteristics of idempotent metrics and provides examples of commutative metric spaces, as well as describes the categories of metrics determined by subsets of X.
JOURNAL OF GEOMETRIC ANALYSIS
(2021)
Article
Computer Science, Theory & Methods
R. A. Bailey, Peter J. Cameron, Michael Kinyon, Cheryl E. Praeger
Summary: This paper explores the scenarios in which a set of partitions, any m of which are minimal elements of a Cartesian lattice, are present. Different mathematical structures such as Latin squares, join-semilattices, and diagonal groups are formed in various cases. It also discusses the structure and applications of abelian groups with specific automorphisms.
DESIGNS CODES AND CRYPTOGRAPHY
(2022)
Article
Optics
Ni Chen, Congli Wang, Wolfgang Heidrich
Summary: In the last decade, holography has made significant progress due to advancements in computational imaging. However, the mismatch between experimental setups and the conceptual model hampers the use of computational tools. This paper presents a novel framework called differentiable holography (partial differential H), which automatically calibrates experimental imperfections in inverse holographic imaging. The technique is demonstrated on auto-focused complex field imaging from a single intensity-only inline hologram.
LASER & PHOTONICS REVIEWS
(2023)
Article
Mathematics
L. Elliott, A. Levine, J. D. Mitchell
Summary: In this note, we establish that the number of monogenic submonoids of the full transformation monoid of degree n for n > 0 is equal to the sum of the number of cyclic subgroups of the symmetric groups on 1 to n points. We also prove a similar statement for monogenic subsemigroups of finite full transformation monoids, as well as monogenic inverse submonoids and subsemigroups of finite symmetric inverse monoids.
COMMUNICATIONS IN ALGEBRA
(2023)
Article
Mathematics
R. A. Bailey, Peter J. Cameron, Cheryl E. Praeger, Csaba Schneider
Summary: This paper focuses on describing and characterizing a type of structure called diagonal semilattices, which belong to the class of finite primitive permutation groups. Unlike other classes, such as affine spaces or Cartesian decompositions, the structures of diagonal semilattices have not been extensively studied. The paper also explores the properties and applications of diagonal semilattices, such as their relationship with partition lattices and their chromatic number.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics
Jimmy Devillet, Pierre Mathonet
Summary: We study the class of symmetric n-ary bands and provide a structure theorem that extends the classical semilattice decomposition of certain bands. The symmetric n-ary bands are exactly the strong n-ary semilattices of n-ary extensions of Abelian groups whose exponents divide n - 1. The necessary and sufficient conditions for a symmetric n-ary band to be reducible to a semigroup are obtained using the structure theorem.
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
(2021)
Article
Astronomy & Astrophysics
Steven Duplij
Summary: This paper generalizes and explores the regularity concept of semigroups, introducing the concepts of higher regularity and higher arity. Through studying the single-relational and multi-relational formulations, it is found that each element in higher regularity has multiple inverses, introducing the concepts of higher idempotents and unique inverses in the multi-relational formulation.
Article
Mathematics
Ivan Kaygorodov, Mykola Khrypchenko
Summary: This article presents an algebraic classification of complex 4-dimensional nilpotent CD-algebras.
LINEAR & MULTILINEAR ALGEBRA
(2022)
Article
Mathematics
M. Dokuchaev, A. Paques, H. Pinedo, I Rocha
Summary: A seven-term exact sequence is provided for partial Galois extensions of commutative rings, generalizing the Chase-Harrison-Rosenberg sequence.
JOURNAL OF ALGEBRA
(2021)
Article
Mathematics, Applied
Mikhailo Dokuchaev, Mykola Khrypchenko, Ganna Kudryavtseva
Summary: This paper discusses the structure and correspondence between partial actions of two-sided restriction semigroups, establishing a connection between proper extensions and partial actions, and defining two isomorphic subcategories in the category of partial actions that are each equivalent to the category of proper extensions.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2021)
Article
Mathematics
Mikhailo Dokuchaev, Arnaldo Mandel, Makar Plakhotnyk
Summary: The article discusses finite quasi semimetrics and their properties on a complete directed graph, including the study of symmetry groups and combinatorial symmetry groups, as well as the special role of integral quasi semimetrics in the theory of tiled orders and the derivation of the automorphism group. These results are based on a more general consideration of polyhedral cones that are closed under componentwise maximum.
DISCRETE MATHEMATICS
(2022)
Article
Mathematics
Erica Z. Fornaroli, Mykola Khrypchenko, Ednei A. Santulo Jr
Summary: In this paper, we study the properness of Lie automorphisms of incidence algebras on finite connected posets. Without any restriction on the length of the poset, we find a sufficient condition related to a certain equivalence relation on the set of maximal chains. For certain classes of posets with length one, we provide a complete answer.
GLASGOW MATHEMATICAL JOURNAL
(2022)
Article
Mathematics
Mykola Khrypchenko
Summary: When the ring R is indecomposable, the R-linear isomorphisms between the partial flag incidence algebras I-3(P,R) and I-3(Q,R) are precisely induced by poset isomorphisms between P and Q. Additionally, the R-linear derivations of I-3(P,R) are trivial.
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
(2022)
Article
Mathematics, Applied
Jorge J. Garces, Mykola Khrypchenko
Summary: This article discusses the incidence algebra of a finite connected poset and describes the bijective linear maps that preserve this algebraic structure. The results show that, under certain conditions, these mappings are either automorphisms or anti-automorphisms, or Lie automorphisms. Moreover, descriptions of mappings that preserve tripotents and k-potents are provided for specific characteristics of the field.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2022)
Article
Mathematics
G. Abrams, M. Dokuchaev, T. G. Nam
Summary: The study demonstrates that the endomorphism ring of a nonzero finitely generated projective module over the Leavitt path algebra is isomorphic to a Steinberg algebra. This extends to show that every nonzero corner of the Leavitt path algebra of any graph is isomorphic to a Steinberg algebra, and any K-algebra with local units Morita equivalent to the Leavitt path algebra of a row-countable graph is isomorphic to a Steinberg algebra as well. Furthermore, it is proven that a corner by a projection of a C*-algebra of a countable graph is isomorphic to the C*-algebra of an ample groupoid.
JOURNAL OF ALGEBRA
(2022)
Article
Mathematics
Mikhailo Dokuchaev, Mykola Khrypchenko, Mayumi Makuta
Summary: This paper defines and studies the concept of a crossed module over an inverse semigroup and its corresponding 4-term exact sequences, known as crossed module extensions. It shows that there is a one-to-one correspondence between equivalence classes of admissible crossed module extensions and elements of the cohomology group H3 <=(T1, A1).
JOURNAL OF ALGEBRA
(2022)
Article
Mathematics, Applied
Amir Fernandez Ouaridi, Ivan Kaygorodov, Mykola Khrypchenko, Yury Volkov
Summary: The paper provides a complete description and classification of primary degenerations and non-degenerations among 3-dimensional, 4-dimensional, and 5-dimensional nilpotent algebras. The considered varieties are shown to be irreducible and determined by specific rigid algebras, with an additional result of an algebraic classification of 4-dimensional complex nilpotent commutative algebras.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2022)
Article
Mathematics
Jorge J. Garces, Mykola Khrypchenko
Summary: This paper studies bijective linear maps that preserve products equal to primitive idempotents, and characterizes the situations in which such maps exist, showing that they are either automorphisms or negative automorphisms of the incidence algebra.
JOURNAL OF ALGEBRA
(2022)
Article
Mathematics, Applied
Ivan Kaygorodov, Mykola Khrypchenko
Summary: We examine transposed Poisson algebra structures on Block Lie algebras B(q) and Block Lie superalgebras S(q), and discover new Lie algebras and superalgebras with non-trivial Hom-Lie algebra structures.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2023)
Article
Mathematics
Erica Z. Fornaroli, Mykola Khrypchenko, Ednei A. A. Santulo Jr
Summary: We fully characterize regular Hom-Lie structures on the incidence algebra I(X, K) of a finite connected poset X over a field K. We prove that such a structure is the sum of a central-valued linear map annihilating the Jacobson radical of I(X, K) with the composition of certain inner and multiplicative automorphisms of I(X, K).
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2023)
Article
Mathematics, Applied
Erica Z. Fornaroli, Mykola Khrypchenko, Ednei A. Santulo
Summary: This article provides a detailed description of the Lie automorphisms of the incidence algebra and shows that they are generally not proper.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
