Fundamentals of Lie theory for [IMG align=ABSMIDDLE alt=$ \mathcal E $]tex_im_3101_img1[/IMG]-structures and some of its applications

Vladimir Vitalyevich Gorbatsevich

doi:10.1070/im9115

Fundamentals of Lie theory for [IMG align=ABSMIDDLE alt=$ \mathcal E $]tex_im_3101_img1[/IMG]-structures and some of its applications

Izvestiya Mathematics ◽

10.1070/im9115 ◽

2022 ◽

Vol 86 (2) ◽

Author(s):

Vladimir Vitalyevich Gorbatsevich

Keyword(s):

Lie Theory

Lie Theory and Special Functions

10.1016/s0076-5392(08)x6124-7 ◽

1968 ◽

Keyword(s):

Special Functions ◽

Lie Theory

Lie theory and the Chern–Weil homomorphism

Annales Scientifiques de l École Normale Supérieure ◽

10.1016/j.ansens.2004.11.004 ◽

2005 ◽

Vol 38 (2) ◽

pp. 303-338 ◽

Cited By ~ 21

Author(s):

A ALEKSEEV ◽

E MEINRENKEN

Keyword(s):

Lie Theory

Lie theory and its applications in control

Systems & Control Letters ◽

10.1016/s0167-6911(01)00089-5 ◽

2001 ◽

Vol 43 (1) ◽

pp. 1

Author(s):

U. Helmke ◽

K. Hüper ◽

J. Lawson

Keyword(s):

Lie Theory

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

Journal of Mathematical Physics ◽

10.1063/1.1666805 ◽

1974 ◽

Vol 15 (8) ◽

pp. 1263-1274 ◽

Cited By ~ 28

Author(s):

E. G. Kalnins ◽

Willard Miller

Keyword(s):

Separation Of Variables ◽

Lie Theory

Basic Differential Equations of Lie Theory

Smooth Homogeneous Structures in Operator Theory - Monographs & Surveys in Pure & Applied Math ◽

10.1201/9781420034806.axb ◽

2005 ◽

pp. 225-270

Keyword(s):

Differential Equations ◽

Lie Theory

Book Review: Lie theory and special functions

Bulletin of the American Mathematical Society ◽

10.1090/s0002-9904-1969-12292-5 ◽

1969 ◽

Vol 75 (5) ◽

pp. 925-928

Author(s):

Louis Weisner

Keyword(s):

Special Functions ◽

Lie Theory

Symmetry analysis of rotating fluid

The ANZIAM Journal ◽

10.1017/s1446181100009779 ◽

2005 ◽

Vol 47 (1) ◽

pp. 65-74 ◽

Cited By ~ 3

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.

Remarks on Quantum Interaction Models by Lie Theory and Modular Forms via Non-commutative Harmonic Oscillators

Mathematics for Industry - A Mathematical Approach to Research Problems of Science and Technology ◽

10.1007/978-4-431-55060-0_2 ◽

2014 ◽

pp. 17-34 ◽

Cited By ~ 2

Author(s):

Masato Wakayama

Keyword(s):

Modular Forms ◽

Harmonic Oscillators ◽

Lie Theory ◽

Interaction Models

Symmetric Systems: Lie Theory

Bilinear Control Systems ◽

10.1023/b101451_2 ◽

2009 ◽

pp. 33-82

Author(s):

David L. Elliott

Keyword(s):

Lie Theory ◽

Symmetric Systems

Lie theory

Analytic Pro-P Groups ◽

10.1017/cbo9780511470882.013 ◽

1999 ◽

pp. 213-240

Keyword(s):

Lie Theory