scholarly journals Lie Algebras of Vector Fields in the Real Plane

1992 ◽  
Vol s3-64 (2) ◽  
pp. 339-368 ◽  
Author(s):  
Artemio González-López ◽  
Niky Kamran ◽  
Peter J. Olver
Keyword(s):  
Lie Algebras ◽  
Vector Fields ◽  
Real Plane ◽  
The Real

scholarly journals Transformation groups on real plane and their differential invariants

2006 ◽  
Vol 2006 ◽  
pp. 1-17 ◽  
Author(s):  
Maryna O. Nesterenko
Keyword(s):  
Lie Algebras ◽  
Differential Invariants ◽  
Transformation Groups ◽  
Real Plane ◽  
Continuous Transformation ◽  
The Real ◽  
Finite Dimensional ◽  
Complete Sets ◽  
Finite Dimensional Lie Algebras ◽  
Invariant Differentiation

Complete sets of bases of differential invariants, operators of invariant differentiation, and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of finite-dimensional Lie algebras on the real plane are revisited.

A Note about Analytic Solvability of Complex Planar Vector Fields with Degeneracies

2011 ◽  
Vol 54 (2) ◽  
pp. 249-254 ◽  
Author(s):  
Paulo L. Dattori da Silva
Keyword(s):  
Special Class ◽  
Vector Fields ◽  
Real Plane ◽  
Complex Vector ◽  
The Real ◽  
Real Curve ◽  
Planar Vector Fields ◽  
Planar Vector ◽  
Analytic Solvability

AbstractThis paper deals with the analytic solvability of a special class of complex vector fields defined on the real plane, where they are tangent to a closed real curve, while off the real curve, they are elliptic.

Level curves of open polynomial functions on the real plane

1994 ◽  
Vol 22 (14) ◽  
pp. 5973-5981
Author(s):  
J. Ferrera ◽  
M.J. de la Puente
Keyword(s):  
Real Plane ◽  
Polynomial Functions ◽  
The Real ◽  
Level Curves

Modal logics of domains on the real plane

Studia Logica ◽  
1983 ◽  
Vol 42 (1) ◽  
pp. 63-80 ◽  
Author(s):  
V. B. Shehtman
Keyword(s):  
Modal Logics ◽  
Real Plane ◽  
The Real

A note on the algebra of Poisson brackets

1984 ◽  
Vol 96 (1) ◽  
pp. 45-60 ◽  
Author(s):  
C. J. Atkin
Keyword(s):  
Poisson Bracket ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Symplectic Manifold ◽  
Vector Fields ◽  
Poisson Brackets ◽  
Infinite Dimensional

In a long sequence of notes in the Comptes Rendus and elsewhere, and in the papers [1], [2], [3], [6], [7], Lichnerowicz and his collaborators have studied the ‘classical infinite-dimensional Lie algebras’, their derivations, automorphisms, co-homology, and other properties. The most familiar of these algebras is the Lie algebra of C∞ vector fields on a C∞ manifold. Another is the Lie algebra of ‘Poisson brackets’, that is, of C∞ functions on a C∞ symplectic manifold, with the Poisson bracket as composition; some questions concerning this algebra are of considerable interest in the theory of quantization – see, for instance, [2] and [3].

Harmonicity of vector fields on a class of Lorentzian solvable Lie groups

2018 ◽  
Vol 18 (3) ◽  
pp. 337-344 ◽  
Author(s):  
Ju Tan ◽  
Shaoqiang Deng
Keyword(s):  
Vector Field ◽  
Lie Groups ◽  
Lie Algebras ◽  
Critical Points ◽  
Vector Fields ◽  
Energy Functional ◽  
Smooth Vector ◽  
Solvable Lie Groups ◽  
Invariant Vector ◽  
Invariant Vector Fields

AbstractIn this paper, we consider a special class of solvable Lie groups such that for any x, y in their Lie algebras, [x, y] is a linear combination of x and y. We investigate the harmonicity properties of invariant vector fields of this kind of Lorentzian Lie groups. It is shown that any invariant unit time-like vector field is spatially harmonic. Moreover, we determine all vector fields which are critical points of the energy functional restricted to the space of smooth vector fields.

scholarly journals Elementary zeros of lie algebras of vector fields

Topology ◽  
1991 ◽  
Vol 30 (2) ◽  
pp. 215-222 ◽  
Author(s):  
J.F. Plante
Keyword(s):  
Lie Algebras ◽  
Vector Fields
Sign in / Sign up

Export Citation Format

Share Document