Article
Mathematics
Arata Minamide, Hiroaki Nakamura
Summary: This paper focuses on determining the automorphism groups of the profinite braid groups with four or more strings, using the profinite Grothendieck-Teichmuller group as a tool.
AMERICAN JOURNAL OF MATHEMATICS
(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
Engineering, Mechanical
Dariusz Mika
Summary: The article introduces a new gradient descent/ascent algorithm for independent component analysis of complex valued data. This algorithm utilizes toral decomposition of the skew Hermitian gradient matrix and a simple and computationally inexpensive projection method based on the Lie structure of optimization landscape. The algorithm was tested and compared to other classes of algorithms, showing superior speed and separation quality, as well as high versatility in terms of cost function applications. The quick response to signal changes characteristic of gradient methods indicates the practical potential of this method in online applications.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Mathematics, Applied
Hamid Darabi, Mehdi Eshrati, Babak Jabbar Nezhad
Summary: This paper discusses the structure and properties of finite dimensional filiform Filippov algebras, including the relationship between the dimension of the Schur multiplier and a non-negative integer associated with the algebra.
RESULTS IN MATHEMATICS
(2021)
Article
Mathematics
Afsaneh Shamsaki, Peyman Niroomand
Summary: In this paper, the authors study finite-dimensional nilpotent Lie algebra L and its minimal number generators for L/Z(L). A formula is provided to calculate the dimension of L/Z(L). The authors classify all finite-dimensional nilpotent Lie algebras L when t(L) is in the set {0, 1, 2} and also find a construction to demonstrate that t(L) can be any integer.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2023)
Article
Physics, Mathematical
Kevin Morand
Summary: This study investigates the action of multi-oriented graph complexes on Lie bialgebroids and their quasi generalizations. By using the cohomology results of (multi)-oriented graphs, the action of the Grothendieck-Teichmuller group on Lie bialgebras and quasi-Lie bialgebras is generalized to quasi-Lie bialgebroids through graphs with two colors, one of them being oriented. It is shown that there is an obstruction to the quantization of a generic Lie bialgebroid in the form of a new Lie(infinity)-algebra structure.
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
(2022)
Article
Mathematics
Naveed Hussain, Stephen S-T Yau, Huaiqing Zuo
Summary: In this article, we study the Lie algebra and local algebra of isolated hypersurface singularities, introducing a new numerical analytic invariant delta(k)(V) and verifying its values in different contexts.
Article
Mathematics
Fuyuan Yang, Qiang Sun, Chao Zhang
Summary: This paper mainly investigates the properties of the Lie graphs defined by finite-dimensional generalized Kac-Moody algebras, and proves the existence of Cayley graphs and Hamiltonian graphs in certain cases. It also constructs a special class of semisymmetric graphs.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2022)
Article
Mathematics
Adela Latorre, Luis Ugarte, Raquel Villacampa
Summary: This article investigates nilpotent Lie algebras of real dimension eight and minimal center that admit a complex structure. Furthermore, for each such nilpotent Lie algebra g, the space of complex structures on g is described up to isomorphism. As an application, the classification of nilpotent Lie algebras with non-trivial abelian J-invariant ideals is provided up to eight dimensions.
JOURNAL OF ALGEBRA
(2023)
Article
Mathematics, Applied
Nicholas W. Mayers, Nicholas Russoniello
Summary: A (2k + 1)-dimensional Lie algebra is called contact if it satisfies the condition ϕ∧(dϕ)k = 0, where ϕ is a one-form. This paper extends recent research and presents a combinatorial procedure for generating contact, type-A Lie poset algebras with chains of arbitrary cardinality in their associated posets. The authors conjecture that their construction provides a complete characterization.
JOURNAL OF GEOMETRY AND PHYSICS
(2023)
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
Physics, Mathematical
Dongfang Gao, Yun Gao
Summary: This paper investigates the planar Galilean conformal algebra G, an infinite-dimensional extension of the finite-dimensional Galilean conformal algebra in (2+1) dimensional space-time. It studies the simple restricted modules over G, including the highest weight modules and Whittaker modules. Simple modules over finite-dimensional solvable Lie algebras are used to construct many simple restricted modules over G. Additionally, several equivalent descriptions for simple restricted modules over G are presented.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Multidisciplinary Sciences
Javier de Lucas, Daniel Wysocki
Summary: This work introduces the concept of the Darboux family, which is used to determine coboundary Lie bialgebras on real four-dimensional, indecomposable Lie algebras in a relatively easy manner. It also classifies them up to Lie algebra automorphisms and discusses r-matrix classification and solutions to classical Yang-Baxter equations. Additionally, a method to obtain matrix representations of certain Lie algebras with a non-trivial center is developed as a byproduct of this work.
Article
Mathematics, Applied
Elsa Dos Santos Cardoso-Bihlo, Roman O. Popovych
Summary: This paper discusses the foundation of modern weather and climate prediction models based on the primitive equations, studying the Lie symmetries and maximal Lie invariance algebra structure. It also explores the mapping of the maximal Lie invariance algebra for a constant Coriolis parameter to the case of vanishing Coriolis force, and the transformation of rotating primitive equations to nonrotating equations through mapping. Additionally, the computation of the complete point symmetry group of the primitive equations using algebraic method is highlighted as another significant result.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mathematics
Dietrich Burde, Wolfgang Alexander Moens
Summary: In this article, we study disemisimple Lie algebras, and prove that the solvable radical of a disemisimple Lie algebra coincides with its nilradical and is a prehomogeneous s-module for a Levi subalgebra. We use the classification of prehomogeneous s-modules for simple Lie algebras to show that the solvable radical of a disemisimple Lie algebra with simple Levi subalgebra is abelian. We also extend this result to disemisimple Lie algebras without simple quotients of type A.
JOURNAL OF ALGEBRA
(2022)
