Input-Output Model Equivalence of Spin Systems: A Characterization Using Lie Algebra Homomorphisms

2008 ◽  
Vol 47 (4) ◽  
pp. 2016-2043 ◽  
Author(s):  
Francesca Albertini ◽  
Domenico D'Alessandro
Keyword(s):  
Lie Algebra ◽  
Spin Systems ◽  
Input Output ◽  
Algebra Homomorphisms ◽  
Model Equivalence

scholarly journals Lifts of Symmetric Tensors: Fluids, Plasma, and Grad Hierarchy

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 907 ◽  
Author(s):  
Oğul Esen ◽  
Miroslav Grmela ◽  
Hasan Gümral ◽  
Michal Pavelka
Keyword(s):  
Kinetic Theory ◽  
Lie Algebra ◽  
Particle Motion ◽  
Evolution Equations ◽  
Poisson Brackets ◽  
Hamiltonian Approach ◽  
Symmetric Tensors ◽  
Field Equations ◽  
Algebra Homomorphisms

Geometrical and algebraic aspects of the Hamiltonian realizations of the Euler’s fluid and the Vlasov’s plasma are investigated. A purely geometric pathway (involving complete lifts and vertical representatives) is proposed, which establishes a link from particle motion to evolution of the field variables. This pathway is free from Poisson brackets and Hamiltonian functionals. Momentum realizations (sections on T * T * Q ) of (both compressible and incompressible) Euler’s fluid and Vlasov’s plasma are derived. Poisson mappings relating the momentum realizations with the usual field equations are constructed as duals of injective Lie algebra homomorphisms. The geometric pathway is then used to construct the evolution equations for 10-moments kinetic theory. This way the entire Grad hierarchy (including entropic fields) can be constructed in a purely geometric way. This geometric way is an alternative to the usual Hamiltonian approach to mechanics based on Poisson brackets.

scholarly journals On the Stability of -Derivations and Lie -Algebra Homomorphisms on Lie -Algebras: A Fixed Points Method

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Seong Sik Kim ◽  
Ga Ya Kim ◽  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Fixed Points ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
The Stability ◽  
Algebra Homomorphisms ◽  
Stability Results

We investigate new generalized Hyers-Ulam stability results for -derivations and Lie -algebra homomorphisms on Lie -algebras associated with the additive functional equation:

scholarly journals The Lie algebra structure and controllability of spin systems

2002 ◽  
Vol 350 (1-3) ◽  
pp. 213-235 ◽  
Author(s):  
Francesca Albertini ◽  
Domenico D'Alessandro
Keyword(s):  
Lie Algebra ◽  
Spin Systems ◽  
Algebra Structure

scholarly journals Multidimensional integrable systems and deformations of Lie algebra homomorphisms

2007 ◽  
Vol 48 (9) ◽  
pp. 093502 ◽  
Author(s):  
Maciej Dunajski ◽  
James D. E. Grant ◽  
Ian A. B. Strachan
Keyword(s):  
Lie Algebra ◽  
Integrable Systems ◽  
Algebra Homomorphisms

Completely positive Lie algebra homomorphisms

2007 ◽  
Vol 88 (6) ◽  
pp. 513-523
Author(s):  
Benedikt Betz
Keyword(s):  
Lie Algebra ◽  
Completely Positive ◽  
Algebra Homomorphisms

scholarly journals Quasispectra of solvable Lie algebra homomorphisms into Banach algebras

2006 ◽  
Vol 174 (1) ◽  
pp. 13-27 ◽  
Author(s):  
Anar Dosiev
Keyword(s):  
Lie Algebra ◽  
Banach Algebras ◽  
Solvable Lie Algebra ◽  
Algebra Homomorphisms

Appendices to chapter 4: F An input/output table

1996 ◽  
pp. 233-253
Keyword(s):  
Input Output ◽  
Output Table

Graphical displays of the motion of spin systems

1996 ◽  
Vol 89 (5) ◽  
pp. 1397-1408 ◽  
Author(s):  
LAWRENCE LOHR
Keyword(s):  
Spin Systems ◽  
Graphical Displays

Input-Output in Personnel Management

1970 ◽  
Vol 15 (2) ◽  
pp. 115, 118
Author(s):  
WILLIAM E. COLEMAN
Keyword(s):  
Personnel Management ◽  
Input Output
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