Article
Physics, Mathematical
Andrei Negut
Summary: The article introduces a method of deforming the W-algebra of gl(nr) through generators and quadratic relations, and demonstrates that the action of the quantum toroidal algebra on the K-theory groups of the moduli spaces of parabolic sheaves factors through the constructed algebra P-n(r).
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
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
Xianguo Hu
Summary: This paper introduces the universal enveloping Hom-algebras of Hom-Poisson algebras and discusses some properties of universal enveloping Hom-algebras of regular Hom-Poisson algebras. Furthermore, it proves the equivalence between the category of involutive Hom-Poisson modules over an involutive Hom-Poisson algebra A and the category of involutive Hom-associative modules over its universal enveloping Hom-algebra U-eh(A).
Article
Physics, Multidisciplinary
Vicente Said Morales-Salgado
Summary: This study investigates deformations of polynomial Heisenberg algebras and establishes a connection with extended affine Weyl groups of type A(m)((1)), contributing to a better understanding of quantum systems and their algebraic structures.
Article
Computer Science, Theory & Methods
I. Yu Mogilnykh
Summary: This article introduces the concept and construction method of propelinear codes, and mentions the action of regular subgroups in the general affine group GA(r, q) and the permutation of cosets of the Hamming code induced by automorphisms.
PROBLEMS OF INFORMATION TRANSMISSION
(2022)
Article
Mathematics, Applied
G. Barbieri, D. Dikranjan, A. Giordano Bruno, H. Weber
Summary: A subgroup H of the circle group T is called a-characterized if there exists a strictly increasing sequence of positive integers (u(n)) n is an element of N-0, with u(n) |u(n+1) for all n is an element of N-0, such that H consists precisely of those elements x is an element of T with u(n)x -> 0 in T. These subgroups appeared in the study of trigonometric series in harmonic analysis, as well as in Diophantine approximation, dynamical systems and ergodic theory. The aim of the paper is to show that any a-characterized subgroup of T can be presented as the sum of two of its proper a-characterized subgroups.
TOPOLOGY AND ITS APPLICATIONS
(2023)
Article
Mathematics, Applied
M. Anoussis, G. K. Eleftherakis, A. Katavolos
Summary: This article investigates the conditions for extending a continuous algebra homomorphism from the Fourier algebra of one locally compact group to the Fourier-Stieltjes algebra of another locally compact group. When the mapping is completely bounded and the original group is amenable, it can be induced by a piecewise affine map. The dual problem is also studied.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics
Osamu Iyama, Rene Marczinzik
Summary: This article proves that the characterization of a lattice being distributive can be given by determining whether its associated incidence algebra is an Auslander regular ring. It also provides an explicit representation of the minimal injective coresolution and a combinatorial formula for the Bass numbers.
ADVANCES IN MATHEMATICS
(2022)
Article
Computer Science, Artificial Intelligence
Safiqul Islam, Arundhati Sanyal, Jayanta Sen
Summary: This paper introduces the concept of topological IL-algebra and generalizes the ideas of topological FLew-algebra, BL-algebra, and MV-algebra. A linear topology is defined on IL-algebra using a system of affine filters, and some properties are achieved. The completion of a topological IL-algebra is obtained with the help of an inverse system of IL-algebras.
Article
Mathematics
Shusuke Otabe, Fabio Tonini, Lei Zhang
Summary: In this paper, we study a purely inseparable counterpart of Abhyankar's conjecture for the affine line in positive characteristic, and prove its validity for all the finite local non-abelian simple group schemes in characteristic p > 5. The key is how to deal with finite local group schemes that cannot be realized as the Frobenius kernel of a smooth algebraic group, such as those associated with Cartan type Lie algebras. We solve this problem for such Lie algebras by utilizing natural gradations or filtrations on them.
MATHEMATISCHE ANNALEN
(2022)
Article
Mathematics
Anak Nongmanee, Sorasak Leeratanavalee
Summary: The study introduces the concept of v-regular ternary Menger algebras of rank n, explores their interesting properties, and investigates the relationship between full n-place functions and left translations.
Article
Mathematics
Katsuyuki Naoi
Summary: The generalized quantum affine Schur-Weyl duality functor establishes an equivalence between two different finite-dimensional module categories, which is of significant importance in the field of algebra.
ADVANCES IN MATHEMATICS
(2021)
Article
Physics, Mathematical
Koichi Betsumiya, Ching Hung Lam, Hiroki Shimakura
Summary: We describe the automorphism groups of all holomorphic vertex operator algebras of central charge 24 with non-trivial weight one Lie algebras by using their constructions as simple current extensions. We also confirm a conjecture of G. Hohn on the numbers of holomorphic vertex operator algebras of central charge 24 obtained as inequivalent simple current extensions of certain vertex operator algebras, which gives another proof of the uniqueness of holomorphic vertex operator algebras of central charge 24 with non-trivial weight one Lie algebras.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Mathematics
Chris Bruce, Xin Li
Summary: We study semigroup C*-algebras of semigroups related to number fields and initial data from class field theory. These semigroup C*-algebras have an interesting C*-algebraic structure, generating new examples of classifiable C*-algebras and exhibiting novel phenomena. Additionally, we utilize K-theoretic invariants to investigate the information encoded in our semigroup C*-algebras about the initial number-theoretic data.
AMERICAN JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics
Maarten Solleveld
Summary: This article investigates the structure of a Bernstein block Rep(G)s in the category of smooth complex G-representations of a reductive p-adic group G, showing that it is almost Morita equivalent with a (twisted) affine Hecke algebra, and can be described using a family of (twisted) graded algebras.
JOURNAL OF ALGEBRA
(2022)
Article
Mathematics
Francesco Catino, Ilaria Colazzo, Paola Stefanelli
JOURNAL OF ALGEBRA
(2016)
Article
Mathematics
Francesco Catino, Ilaria Colazzo, Paola Stefanelli
JOURNAL OF ALGEBRA
(2017)
Article
Mathematics, Applied
Francesco Catino, Ilaria Colazzo, Paola Stefanelli
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
(2019)
Article
Mathematics, Applied
Marco Castelli, Francesco Catino, Maria Maddalena Miccoli, Giuseppina Pinto
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
(2019)
Article
Mathematics, Applied
M. Castelli, F. Catino, G. Pinto
JOURNAL OF PURE AND APPLIED ALGEBRA
(2019)
Article
Mathematics
F. Catino, M. Mazzotta, M. M. Miccoli
COMMUNICATIONS IN ALGEBRA
(2020)
Article
Mathematics, Applied
Francesco Catino, Ilaria Colazzo, Paola Stefanelli
JOURNAL OF PURE AND APPLIED ALGEBRA
(2020)
Article
Mathematics
Marco Castelli, Francesco Catino, Giuseppina Pinto
COMMUNICATIONS IN ALGEBRA
(2020)
Article
Mathematics, Applied
Francesco Catino, Ilaria Colazzo, Paola Stefanelli
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2020)
Article
Mathematics
Francesco Catino, Marzia Mazzotta, Paola Stefanelli
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
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: 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
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
M. Castelli, F. Catino, G. Pinto
COMMUNICATIONS IN ALGEBRA
(2018)
