We study generalized Lie bialgebroids over a single point, that is, generalized Lie bialgebras. Lie bialgebras are examples of generalized Lie bialgebras. Moreover, we prove that the last ones can be considered as the infinitesimal invariants of Lie groups endowed with a certain type of Jacobi structures. We also propo…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
Trend · papers per month
48 results for “Lie method”
New Lie-group methods preserve geometric divergence-free features on manifolds.
problem Designing divergence-free Lie-group methods on manifolds.
method Introducing planar aromatic trees to span the free tracial post-Lie-Rinehart algebra.
result New Lie-group methods derived for high-order accuracy.
A study is made of real Lie algebras admitting a hypersymplectic structure, and we provide a method to construct such hypersymplectic Lie algebras. We use this method in order to obtain the classification of all hypersymplectic structures on four-dimensional Lie algebras, and we describe the associated metrics on the c…
Lie algebroids and curved Lie algebras are equivalent categories.
problem Understanding the relationship between Lie algebroids and curved Lie algebras.
method Developed a method to study the -category of curved Lie algebras using homotopy theory of algebras over a complete operad.
result Equivalence of -categories between Lie algebroids and certain kinds of curved Lie algebras.
Method constructs complex symplectic Lie algebras from simpler ones.
problem Classifying complex symplectic Lie algebras of various dimensions.
method Complex symplectic oxidation method
result Classification of eight-dimensional nilpotent complex symplectic Lie algebras.
Study on pseudo-Hermitian quadratic nilpotent Lie algebras with methods and classifications.
problem Characterizing and classifying pseudo-Hermitian quadratic nilpotent Lie algebras.
method Construction methods and double extension by planes.
result Complete classification of nilpotent quadratic Lie algebras and pseudo-Hermitian metrics up to dimension 8.
New method constructs nilpotent Lie algebras from quivers.
problem Constructing nilpotent Lie algebras from quivers.
method Using paths within quivers to construct nilpotent Lie algebras.
result Constructs a broad family of Ricci soliton nilmanifolds.
A Lie system is the non-autonomous system of differential equations describing the integral curves of a non-autonomous vector field taking values in a finite-dimensional Lie algebra of vector fields, a so-called Vessiot--Guldberg Lie algebra. This work pioneers the analysis of Lie systems admitting a Vessiot--Guldberg …
New method constructs Ricci-flat metrics on Lie groups.
problem Finding Ricci-flat metrics on Lie groups.
method Combinatorial method to construct indefinite Ricci-flat metrics.
result Infinite families of Ricci-flat nilmanifolds constructed.
The study analyzes stochastic Lie systems and their applications in various models.
problem Analyzing stochastic differential equations on manifolds.
method Coalgebra method for Hamiltonian stochastic Lie systems.
result New examples of stochastic Lie systems and Hamiltonian stochastic Lie systems are analyzed.
New method finds Lie group representations without explicit groups, enabling new neural network architectures.
problem Building neural networks equivariant to arbitrary Lie groups.
method Algorithm to find Lie group representations from Lie algebra structure constants. Self-contained method for constructing Lie group-equivariant neural networks.
result First object-tracking model equivariant to the Poincaré group.
New method solves Cartan's problem for Lie algebroids and groupoids.
problem Classification of extremal Kähler metrics on surfaces.
method New theory of Lie algebroids and groupoids with structure group and connection.
result Local and complete solutions, symmetries, and moduli spaces determined.
Paper corrects and expands stochastic Lie systems theory.
problem Stochastic Lie systems and their properties.
method Corrected stochastic Lie theorem, introduced new stochastic Lie systems.
result Stochastic Lie systems can differ significantly between Stratonovich and Itô approaches.
Spatio-temporal Lie-Poisson discretization for incompressible magnetohydrodynamics on the spheremath.NA
New method preserves MHD equations on sphere without costly matrix exponentials.
problem Discretizing MHD equations on sphere for numerical simulations.
method Lie-Poisson discretization, geometric quantization, semi-direct product Lie algebras.
result Preserves Lie-Poisson structure and Casimir functions.
Proves integrability of strict Lie 2-algebras using cohomological methods.
problem Integrability of strict Lie 2-algebras.
method Van Est theorems relating cohomologies of Lie 2-groups and algebras.
result Proves integrability of Lie 2-algebras.
We give a method to obtain new 7-dimensional Lie algebras endowed with closed and coclosed G2-structures starting from 6-dimensional Lie algebras with symplectic half- at SU(3)-structures and half- at SU(3)- structures, respectively. Finally, we describe all the 7-dimensional Lie algebras with a closed G2-structure tha…
Classifies Lie bialgebras using Darboux families.
problem Classifying real four-dimensional indecomposable coboundary Lie bialgebras.
method Introducing Darboux families to classify Lie bialgebras geometrically.
result Classification of coboundary Lie bialgebras on real four-dimensional indecomposable Lie algebras.
This paper studies actions of solvable Lie groups on nilpotent Lie groups.
problem Characterizing which solvable Lie groups can act simply transitively on nilpotent Lie groups.
method Using Lie algebra properties and semisimple splitting, the paper provides methods to check for such actions.
result A full description of possibilities for actions up to dimension 4.
Develops Lie algebraic approach for compact complex homogeneous manifolds.
problem Proves important results on compact complex homogeneous manifolds.
method Uses standard results in Lie theory to associate a canonical abelian Lie algebra with a given integrable complex structure.
result Provides a new method of associating a canonical abelian Lie algebra with a given integrable complex structure.
Lie PCA improves density estimation on symmetric manifolds.
problem Density estimation for symmetric manifolds.
method Spectral method to approximate Lie algebra of symmetry group.
result Improved sample complexity and density estimation on various data sets.
Variational Optimization on Lie Groups, with Examples of Leading (Generalized) Eigenvalue Problemscs.LG
Optimizes functions on Lie groups using generalized eigenvalue problems.
problem Optimization on Lie groups with specific applications to eigenvalue problems.
method Generalizes NAG principle to Lie groups, resulting in continuous Lie-NAG dynamics converging to local optima.
result Discretized Lie-NAG dynamics yield structure-preserving optimization algorithms with faithful energy behavior.
Constructs integrable systems for Lie-Poisson structures at nilpotent elements.
problem Integrability of transverse Lie-Poisson structures at nilpotent elements.
method Using the argument shift method to construct families of functions in involution.
result Provides a uniform construction of completely integrable systems for an infinite family of nilpotent elements.
Abstract: New methods for finding optimal controls in geometric problems on Lie groups.
problem Finding optimal controls for geodesics on Lie groups.
method Pontryagin maximum principle, (co)adjoint representation, geodesic vector field.
result Developed methods to find normal geodesics and locally optimal controls.
Geometric methods integrate Lie systems for optimal control problems.
problem Integrating Lie systems for optimal control problems.
method Geometric numerical methods based on Magnus expansions and Runge-Kutta-Munthe-Kaas.
result Accurate numerical solutions for Lie systems in optimal control problems.
Extends Cheeger's method to Lie groupoid actions on manifolds.
problem Smooth Lie group actions on manifolds with singularities.
method Extension of Cheeger's deformation techniques to Lie groupoid actions.
result Explicit sectional curvature description of the deformation.
Uniform Lie algebras are combinatorially defined two-step nilpotent Lie algebras which can be used to define Einstein solvmanifolds. These Einstein spaces often have nontrivial isotropy groups. We derive basic properties of uniform Lie algebras and we classify uniform Lie algebras with five or fewer generators. We defi…
In this paper we introduce two new methods for constructing harmonic morphisms from solvable Lie groups. The first method yields global solutions from any simply connected nilpotent Lie group and from any Riemannian symmetric space of non-compact type and rank . The second method provides us with global solutio…
New method for constructing contact Lie systems on various spaces.
problem Constructing contact Lie systems on Riemannian and Lorentzian spaces.
method Adaptation of scaling symmetries to Lie-Hamilton systems, leading to contact Lie systems.
result Curvature-dependent reductions of contact Lie systems on Cayley-Klein spaces.
Study index theory on Lie group homogeneous spaces using topological and analytic methods.
problem Index theory on homogeneous spaces of Lie groups.
method Topological and analytic approaches: Riemann-Roch formula and heat kernel methods.
result Local index formula representing higher indices of equivariant elliptic operators.
Study non-integer power-law potentials for Schrödinger operators using Lie-Rinehart algebras.
problem Analyzing Schrödinger operators with non-integer power-law potentials.
method Using Lie-Rinehart algebras and microlocal analysis.
result Microlocal analysis can be applied to Schrödinger operators with non-integer power-law potentials.
Lie groups of automorphisms of cotangent bundles of Lie groups are completely characterized and interesting results are obtained. We give prominence to the fact that the Lie groups of automorphisms of cotangent bundles of Lie groups are super symmetric Lie groups. In the cases of orthogonal Lie lgebras, semi-simple Lie…
New method for moment maps in multisymplectic geometry using Lie 2-algebras.
problem Existence and construction of moment maps in multisymplectic geometry.
method Introducing homotopy moment maps defined on a Lie 2-algebra.
result Existence criteria and construction of homotopy moment maps.
The paper develops methods to derive mixed superposition rules for Lie systems and applies them to various physical systems.
problem Finding general solutions for Lie systems.
method Develops mixed superposition rules for Lie systems with imprimitive Lie algebras and semidirect sums.
result Extends coalgebra method to Lie systems of partial differential equations.
We generalize the Uhlenbeck-Segal theory for harmonic maps into compact semi-simple Lie groups to general Lie groups equipped with torsion free bi-invariant connection.
We consider a method popular in the literature of associating a two-step nilpotent Lie algebra with a finite simple graph. We prove that the two-step nilpotent Lie algebras associated with two graphs are Lie isomorphic if and only if the graphs from which they arise are isomorphic.
A notion of n-Lie algebra introduced by V.T. Filippov can be viewed as a generalization of a concept of binary Lie algebra to the algebras with n-ary multiplication law. A notion of Lie algebra can be extended to Z_2-graded structures giving a notion of Lie superalgebra. Analogously a notion of n-Lie algebra can be ext…
Paper finds non-positive Weyl connections on Lie groups, confirming a conjecture.
problem Finding non-positive invariant Weyl connections on Lie groups.
method Investigation of completely solvable Lie groups, focusing on SOL group.
result Only SOL admits non-positive Weyl connections, confirming a conjecture.
The paper studies efficient Hessian fitting methods for stochastic optimization.
problem Efficient Hessian fitting for stochastic optimization.
method Preconditioned Stochastic Gradient Descent (PSGD) method and Lie groups.
result Hessian fitting problem is strongly convex in certain Lie groups.
We give a new method for manufacturing complete minimal submanifolds of compact Lie groups and their homogeneous quotient spaces. For this we make use of harmonic morphisms and basic representation theory of Lie groups. We then apply our method to construct many examples of compact minimal submanifolds of the special u…
In the present paper we study the Lie sphere geometry of Legendre surfaces by the method of moving frame and we prove an existence theorem for real-analytic Lie-minimal Legendre surfaces.
Study LCS structures of the second kind on Lie algebras.
problem Characterize and construct LCS Lie algebras.
method Construct new examples using representations and characterize existing ones.
result Characterize all LCS Lie algebras obtained with the construction.
New methods find Ricci-flat metrics on specific Lie groups.
problem Finding Ricci-flat metrics on Lie groups.
method Two constructions based on gradings and filtrations.
result Every nilpotent Lie algebra of dimensions up to 9 admits an indefinite Ricci-flat metric.
This work concerns the definition and analysis of a new class of Lie systems on Poisson manifolds enjoying rich geometric features: the Lie--Hamilton systems. We devise methods to study their superposition rules, time independent constants of motion and Lie symmetries, linearisability conditions, etc. Our results are i…
On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from su(2) to e(2), the Lie algebra of upper-triangular matrices with ze…
New methods for solving hydrodynamic-type equations using quasi-rectifiable Lie algebras.
problem Solving systems of hydrodynamic-type equations.
method Introducing and analyzing quasi-rectifiable Lie algebras and vector fields.
result New methods for solving hydrodynamic-type equations.
Study of curves in Lie sphere geometry using moving frames and variational principles.
problem Characterize curves in Lie sphere geometry using Lie curvatures.
method Moving frames, exterior differential systems, and calculus of variations.
result Critical curves are uniquely determined by Lie curvatures.
Lie Symmetry Classification and Numerical Analysis of KdV Equation with Power-law Nonlinearitymath.DG
In this paper, a complete Lie symmetry analysis of the damped wave equation with time-dependent coefficients is investigated. Then the invariant solutions and the exact solutions generated from the symmetries are presented. Moreover, a Lie algebraic classifications and the optimal system are discussed. Finally, using C…
We characterize H-like Lie algebras in terms of subspaces of cones over conjugacy classes in , translating the classification problem for H-like Lie algebras to an equivalent problem in linear algebra. We study properties of H-like Lie algebras, present new methods for constructing them, in…