Article
Physics, Multidisciplinary
Joaquim Gomis, Axel Kleinschmidt
Summary: This paper investigates the kinematic algebras realized on geometric spaces and their constraints on physical models. The authors develop a framework that systematically captures the corrections to the strict non-relativistic limit and introduce new infinite-dimensional algebras. The realization of these algebras using particle models highlights a new type of duality between the Galilei and Carroll limits.
FRONTIERS IN PHYSICS
(2022)
Article
Mathematics
Doston Jumaniyozov, Bakhrom Omirov
Summary: In this paper, we introduce skew-symmetric n-ary brackets on an associative commutative algebra and provide several new examples of n-Lie algebras, some of which are simple n-Lie algebras.
LINEAR & MULTILINEAR ALGEBRA
(2023)
Article
Mathematics
Mikhail Ignatyev, Alexey Petukhov
Summary: The paper discusses the universal enveloping algebra and symmetric algebra of a locally nilpotent infinite-dimensional Lie algebra over C, with a focus on their primitive and Poisson spectra. It provides a homeomorphism between the corresponding topological spaces and shows that primitive ideals of S(n) are mostly generated by intersections with the Poisson center. Additionally, the paper presents two criteria for determining nonzero primitive ideals in the context of nil-Dynkin Lie algebras.
JOURNAL OF ALGEBRA
(2021)
Article
Mathematics
Helge Gloeckner, Joachim Hilgert
Summary: In this paper, we develop certain aspects of geometric control theory on Lie groups G, including the infinite-dimensional case, and on smooth G-manifolds M modeled on locally convex spaces. We utilize time-dependent fundamental vector fields that are L-1 in time to examine the existence and uniqueness of differential equations on M. We also explore the closures of reachable sets in M for controls in the Lie algebra of G or within a compact convex subset of g, with the regularity properties of Lie group G playing a crucial role.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Oksana Bezushchak, Waldemar Holubowski, Bogdana Oliynyk
Summary: This passage mainly discusses the classification of ideals in the Lie algebra of all linear transformations on an infinite-dimensional vector space over a field with characteristic not equal to 2.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Engineering, Multidisciplinary
A. Hussain, M. Usman, Hala M. E. Ahmed, T. F. Ibrahim, Ranya A. Tahir, Ahmed M. Hassan
Summary: This article explores the wave dynamics of a (3+1)-dimensional nonlinear model, which represents shallow water waves. This model is relevant for understanding phenomena such as tides, storms, atmospheric flows, and tsunamis. The Lie group method is used to obtain precise solutions to nonlinear partial differential equations in various domains. Its applications span across mathematical physics, nonlinear dynamics, oceanography, and engineering sciences. 2D and 3D graphs are generated to illustrate the physical implications of specific solutions.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Physics, Multidisciplinary
Manjit Singh
Summary: This study examines the integrability of an eighth-order equation in (3 + 1) dimension, revealing that its symmetry group is infinite-dimensional and confirming the presence of a Virasoro-like structure. It is demonstrated that the equation does not possess the Painleve property, and provides one- and two-dimensional classifications for the infinite-dimensional symmetry algebra.
PRAMANA-JOURNAL OF PHYSICS
(2022)
Article
Mathematics
Simon Machado
Summary: The study investigates infinite approximate subgroups of soluble Lie groups, showing their proximity to genuine connected subgroups in a defined sense. Building on this, a structure theorem for approximate lattices in soluble Lie groups is proved, extending Yves Meyer's theorem on quasi-crystals to the context of soluble Lie groups.
MATHEMATISCHE ANNALEN
(2022)
Article
Mathematics
Tomas Ibarlucia
Summary: The study shows that large topological groups within a distinguished class, Roelcke precompact Polish groups, have Kazhdan's Property (T) and provides specific examples of such groups.
INVENTIONES MATHEMATICAE
(2021)
Article
Mathematics
Mahya Ghandehari, Hun Hee Lee, Jean Ludwig, Nico Spronk, Lyudmila Turowska
Summary: The study focuses on Beurling-Fourier algebras with weights on various Lie groups and their spectral analysis. A refined general definition of weights on the dual of locally compact groups and their associated Beurling-Fourier algebras is introduced. The spectrum of Beurling-Fourier algebras on representative examples of Lie groups is determined, emphasizing the connection to the complexification of underlying Lie groups, and it is shown that polynomially growing weights do not change the spectrum and maintain regularity.
ADVANCES IN MATHEMATICS
(2021)
Article
Mathematics
K. K. Abdurasulov, B. A. Omirov, I. S. Rakhimov, G. O. Solijanova
Summary: The paper investigates the class of all solvable extensions of an infinite-dimensional filiform Leibniz algebra, where the second cohomology group of the extension is proven to be trivial.
JOURNAL OF ALGEBRA
(2021)
Article
Mathematics
Limeng Xia, Dong Liu
Summary: This paper classifies all finite dimensional simple modules over the GIM Lie algebra Q(n+1) (2, 1) and Theta(2n+1), which are more complex in structure and have posed new difficulties in studying their representation theory.
Article
Mathematics
Kenro Furutani, Irina Markina
Summary: In this paper, we determine the group of automorphisms of pseudo H-type Lie algebras, which are two step nilpotent Lie algebras closely related to the Clifford algebras.
JOURNAL OF ALGEBRA
(2021)
Article
Engineering, Mechanical
Peng Sun, Yanbiao Li, Ke Chen, Wentao Zhu, Qi Zhong, Bo Chen
Summary: Advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms, leading to the development of a generalized analysis method and a concise kinematics transfer matrix. The study explores the basic principles of Lie groups and Lie algebras to derive a method for kinematics analysis of parallel mechanisms, formulating Jacobian matrix and Hessian matrix recursively. The proposed method for kinematics analysis of hybrid mechanisms is shown to be practically feasible through a simulation experiment on a humanoid hybrid robotic arm.
CHINESE JOURNAL OF MECHANICAL ENGINEERING
(2021)
Article
Mathematics, Applied
Ingrid Beltita, Daniel Beltita
Summary: The paper provides an explicit description of the tracial state simplex of the C*-algebra C*(G) of a connected, second countable, locally compact, solvable group G. It is shown that every tracial state of C*(G) can be derived from a tracial state of the C*-algebra of the abelianized group, and the intersection of the kernels of all tracial states forms a proper ideal unless G is abelian. Consequently, the C*-algebra of a connected solvable nonabelian Lie group cannot embed into a simple unital AF-algebra.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
