Graded manifolds, graded Lie theory, and prequantization

1977 ◽  
pp. 177-306 ◽  
Author(s):  
Bertram Kostant
Keyword(s):  
Lie Theory ◽  
Graded Manifolds

scholarly journals Higher Dimensional Holonomy Map for Rules Submanifolds in Graded Manifolds

2020 ◽  
Vol 8 (1) ◽  
pp. 68-91
Author(s):  
Gianmarco Giovannardi
Keyword(s):  
Characteristic Direction ◽  
Fixed Degree ◽  
One Dimensional ◽  
First Order ◽  
Natural Choice ◽  
Higher Dimensional ◽  
Graded Manifold ◽  
The One ◽  
Graded Manifolds ◽  
Holonomy Map

AbstractThe deformability condition for submanifolds of fixed degree immersed in a graded manifold can be expressed as a system of first order PDEs. In the particular but important case of ruled submanifolds, we introduce a natural choice of coordinates, which allows to deeply simplify the formal expression of the system, and to reduce it to a system of ODEs along a characteristic direction. We introduce a notion of higher dimensional holonomy map in analogy with the one-dimensional case [29], and we provide a characterization for singularities as well as a deformability criterion.

scholarly journals Lie theory and the Chern–Weil homomorphism

2005 ◽  
Vol 38 (2) ◽  
pp. 303-338 ◽  
Author(s):  
A ALEKSEEV ◽  
E MEINRENKEN
Keyword(s):  
Lie Theory

Lie theory and its applications in control

2001 ◽  
Vol 43 (1) ◽  
pp. 1
Author(s):  
U. Helmke ◽  
K. Hüper ◽  
J. Lawson
Keyword(s):  
Lie Theory

scholarly journals Lie theory and separation of variables. 4. The groups SO (2,1) and SO (3)

1974 ◽  
Vol 15 (8) ◽  
pp. 1263-1274 ◽  
Author(s):  
E. G. Kalnins ◽  
Willard Miller
Keyword(s):  
Separation Of Variables ◽  
Lie Theory

scholarly journals Symmetry analysis of rotating fluid

2005 ◽  
Vol 47 (1) ◽  
pp. 65-74 ◽  
Author(s):  
K. Fakhar ◽  
Zu-Chi Chen ◽  
Xiaoda Ji
Keyword(s):  
Steady State ◽  
Infinite Number ◽  
Special Function ◽  
Equations Of Motion ◽  
Time Dependent ◽  
Lie Theory ◽  
Rotating Fluid ◽  
Type Solution ◽  
Function Type ◽  
Basic Equations

AbstractThe machinery of Lie theory (groups and algebras) is applied to the unsteady equations of motion of rotating fluid. A special-function type solution for the steady state is derived. It is then shown how the solution generates an infinite number of time-dependent solutions via three arbitrary functions of time. This algebraic structure also provides the mechanism to search for other solutions since its character is inferred from the basic equations.

Symmetric Systems: Lie Theory

2009 ◽  
pp. 33-82
Author(s):  
David L. Elliott
Keyword(s):  
Lie Theory ◽  
Symmetric Systems
Sign in / Sign up

Export Citation Format

Share Document