Article
Mathematics, Applied
Huidong Wang, Chunguang Xia, Xiufu Zhang
Summary: In this paper, the non-weight representations of two classes of Lie algebras and two classes of Block type Lie superalgebras are studied. The free U(h)-modules of rank one or two over these Lie superalgebras are completely classified and the simplicity and isomorphism classes of these modules are determined. Additionally, the non-weight representation results for a class of non-semisimple finitely graded extensions of the Virasoro algebra are obtained.
JOURNAL OF GEOMETRY AND PHYSICS
(2023)
Article
Mathematics
Ying Wu, Huidong Wang, Chunguang Xia
Summary: This article introduces a class of Lie conformal superalgebras and discusses the classification of their free conformal modules and finite irreducible conformal modules.
COMMUNICATIONS IN ALGEBRA
(2023)
Article
Mathematics
Bruno Leonardo Macedo Ferreira, Ivan Kaygorodov, Viktor Lopatkin
Summary: This study establishes a relationship between 1/2-derivations of Lie algebras and transposed Poisson algebras, exploring the connection between some non-trivial transposed Poisson algebras and specific Lie algebras.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2021)
Article
Mathematics
Yang Chen, Kaiming Zhao, Yueqiang Zhao
Summary: In this paper, it is proven that every local derivation on Witt algebras is a derivation, and as a consequence, it is also shown that every local derivation on a centerless generalized Virasoro algebra of higher rank is a derivation.
LINEAR & MULTILINEAR ALGEBRA
(2022)
Article
Mathematics
Mengjun Wang, Zhixiang Wu
Summary: This article introduces the concept of Schrodinger-Virasoro Lie conformal algebras and studies and classifies them using pseudoalgebra language.
COMMUNICATIONS IN ALGEBRA
(2023)
Article
Mathematics
Yucai Su, Xiaoqing Yue
Summary: In this paper, the authors classify a class of Z-graded simple Lie conformal algebras that cannot be embedded into any general Lie conformal algebra, including some Lie conformal algebras of Block type.
JOURNAL OF ALGEBRA
(2021)
Article
Mathematics
Lamei Yuan, Qianyi Hua
Summary: This paper introduces the concept of a delta-biderivation, explores its properties, and discusses its applications in various algebraic structures. The study reveals the relationship between 1/2-biderivations and transposed Poisson algebras, and provides examples of Lie algebras with nontrivial transposed Poisson algebra structures.
LINEAR & MULTILINEAR ALGEBRA
(2022)
Article
Mathematics, Applied
Ivan Kaygorodov, Mykola Khrypchenko
Summary: This paper studies transposed Poisson structures on generalized Witt algebras W(A, V, <., .>) and Block Lie algebras L(A, g, f) over a field F of characteristic zero, where <., .> and f are non-degenerate. Specifically, it is shown that all transposed Poisson algebra structures on W(A, V, <., .>) are trivial when dim(V) > 1, and when dim(V) = 1, these structures are mutations of the group algebra structure on FA. The transposed Poisson algebra structures on L(A, g, f) are in one-to-one correspondence with commutative and associative multiplications defined on a complement of the square of L(A, g, f) with values in the center of L(A, g, f). These results generalize earlier findings about transposed Poisson structures on Block Lie algebras B(q).
RESULTS IN MATHEMATICS
(2023)
Article
Mathematics, Applied
Ivan Kaygorodov, Mykola Khrypchenko
Summary: We describe 12-derivations and transposed Poisson algebra structures on Witt type Lie algebras V(f), where f: Gamma -> C is non-trivial and f(0)=0. The study shows that when |f(Gamma)| >= 4, all transposed Poisson algebra structures on V(f) are mutations of the group algebra structure (V(f),middot). When |f(Gamma)| = 3, the direct sum of 3 subspaces of V(f) is obtained, corresponding to cosets of Gamma 0 in Gamma, with different mutations of middot as multiplications. For the case |f(Gamma)| = 2, more complicated mutations of middot are involved. This study also identifies new Lie algebras that have non-trivial Hom-Lie algebra structures.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2023)
Article
Mathematics
Valentina Iusa, Sandro Mattarei, Claudio Scarbolo
Summary: The article discusses infinite-dimensional graded Lie algebras, classifying them based on specific characteristics and generating elements, and makes significant progress in the study.
JOURNAL OF ALGEBRA
(2021)
Article
Mathematics
Sandro Mattarei, Simone Ugolini
Summary: This study lays the foundation for the classification of algebras of arbitrary type n, with the main result describing all possibilities for the first constituent length of an algebra of type n, closely related to the dimension of its largest metabelian quotient.
JOURNAL OF ALGEBRA
(2022)
Article
Mathematics
Chengming Bai, Ruipu Bai, Li Guo, Yong Wu
Summary: We introduce a dual notion of the Poisson algebra, called the transposed Poisson algebra, by exchanging the roles of the two binary operations in the Leibniz rule defining the Poisson algebra. The transposed Poisson algebra shares common properties of the Poisson algebra and arises naturally from a Novikov-Poisson algebra by taking the commutator Lie algebra of the Novikov algebra. The transposed Poisson algebra captures the algebraic structures when the commutator is taken in pre-Lie Poisson algebras and two other Poisson type algebras.
JOURNAL OF ALGEBRA
(2023)
Article
Mathematics
Munayim Dilxat, Shoulan Gao, Dong Liu, Limeng Xia
Summary: This paper focuses on a class of non-weight modules over the Lie algebra of the Weyl type, and explores the construction, characterization, and investigation of modules over the differential operator algebra and the differential operator algebra of multi-variables.
Article
Mathematics
Kun Wang, Shanshan Qi, Haitao Ma, Zhujun Zheng
Summary: This paper introduces the concept of stability of a sequence of modules over Hecke algebras and proves that a finitely generated consistent sequence of representations of Hecke algebras is representation stable.
Article
Mathematics, Applied
Maosen Xu, Yanyong Hong
Summary: In this paper, the notion of completely non-trivial module of a Lie conformal algebra is introduced, and finite irreducible modules of a class of graded Lie conformal algebras are classified. It is shown that all non-trivial finite irreducible modules of these algebras are free of rank one as a C [partial derivative]-module.
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)