Geometry of Riccati equations over normed division algebras
type: Item
instance of: scholarly article
title: Geometry of Riccati equations over normed division algebras
zbMATH Open document ID: 1381.34030
published in: Journal of Mathematical Analysis and Applications
publication date: 2016-04-18T00:00:00Z
full work available at URL: https://arxiv.org/abs/1603.01413
Mathematics Subject Classification ID: 34A26
Mathematics Subject Classification ID: 17A35
Mathematics Subject Classification ID: 17B66
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 35Q40
zbMATH DE Number: 6570301
zbMATH Keywords: Lie system
zbMATH Keywords: normed division algebra
zbMATH Keywords: octonion
zbMATH Keywords: quaternion quantum mechanics
zbMATH Keywords: Riccati equation
zbMATH Keywords: Vessiot-Guldberg Lie algebra
author: J. de Lucas
author: M. Tobolski
author: S. Vilarino
MaRDI profile type: Publication
OpenAlex ID: W2301346789
arXiv ID: 1603.01413
cites work: Quaternionic quantum field theory
cites work: Q3127106
cites work: The octonions
cites work: From constants of motion to superposition rules for Lie-Hamilton systems
cites work: The Riccati equation
cites work: Lie–Hamilton systems on the plane: applications and superposition rules
cites work: A Remark About the Lie Algebra of Infinitesimal Conformal Transformations of the Euclidean Space
cites work: Conformal geometry of surfaces in \(S^4\) and quaternions
cites work: Möbius Transformations and Periodic Solutions of Complex Riccati Equations
cites work: Lie systems: theory, generalisations, and applications
cites work: Lie-Hamilton systems: theory and applications
cites work: Superposition rules, Lie theorem, and partial differential equations
cites work: Generalized coherent states for time-dependent and nonlinear Hamiltonian operators via complex Riccati equations
cites work: Wei-Norman equations for a unitary evolution
cites work: Primitive subalgebras of complex Lie algebras. I: Primitive subalgebras of the classical complex Lie algebras
cites work: Time-evolution of quantum systems via a complex nonlinear Riccati equation. I: Conservative systems with time-independent Hamiltonian
cites work: Quaternionic potentials in non-relativistic quantum mechanics
cites work: A new application of k-symplectic Lie systems
cites work: \(k\)-symplectic Lie systems: theory and applications
cites work: The Geometry of the Octonions
cites work: Q5720933
cites work: Lie symmetries for Lie systems: applications to systems of ODEs and PDEs
cites work: Symmetry and quaternionic integrable systems
cites work: Lie Algebras of Vector Fields in the Real Plane
cites work: On a quaternionic analogue of the cross-ratio
cites work: Structure and Geometry of Lie Groups
cites work: Q5843703
cites work: Q4262007
cites work: Composition algebras and their automorphisms
cites work: On a Possible Generalization of Quantum Mechanics
cites work: On a complex differential Riccati equation
cites work: On the reduction of the multidimensional stationary Schrödinger equation to a first-order equation and its relation to the pseudoanalytic function theory
cites work: Applied Pseudoanalytic Function Theory
cites work: Q4546455
cites work: New further integrability cases for the Riccati equation
cites work: Newton's laws of motion in the form of a Riccati equation
cites work: Simple subgroups of simple Lie groups and nonlinear differential equations with superposition principles
cites work: Conjugacy classification of quaternionic Möbius transformations
cites work: Q3812860
cites work: Explicit solutions of the \({\mathfrak{a}_1}\)-type Lie-Scheffers system and a general Riccati equation
cites work: Q4003413
cites work: A mathematical introduction to conformal field theory. Based on a series of lectures given at the Mathematisches Institut der Universität Hamburg
cites work: Classification of systems of nonlinear ordinary differential equations with superposition principles
cites work: A Lie Theoretic Approach to Thompson's Theorems on Singular Values-Diagonal Elements and Some Related Results
cites work: Q4201879
cites work: Quaternionic-valued ordinary differential equations. The Riccati equation
cites work: Q3688669
DOI: 10.1016/J.JMAA.2016.03.031
description: scientific article; zbMATH DE number 6570301