Racah Problems for the Oscillator Algebra, the Lie Algebra $$\mathfrak {sl}_n$$, and Multivariate Krawtchouk Polynomials

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

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Reduction of partially invariant submodels of rank 3 defect 1 to invariant submodels

Multiphase Systems ◽

10.21662/mfs2018.3.009 ◽

2018 ◽

Vol 13 (3) ◽

pp. 59-63 ◽

Cited By ~ 1

Author(s):

D.T. Siraeva

Keyword(s):

Equation Of State ◽

Lie Algebra ◽

Lie Algebras ◽

Gas Dynamics ◽

Hydrodynamic Type ◽

System Of Equations ◽

Two Dimensional ◽

Equations Of Gas Dynamics ◽

Entropy Functions

Equations of hydrodynamic type with the equation of state in the form of pressure separated into a sum of density and entropy functions are considered. Such a system of equations admits a twelve-dimensional Lie algebra. In the case of the equation of state of the general form, the equations of gas dynamics admit an eleven-dimensional Lie algebra. For both Lie algebras the optimal systems of non-similar subalgebras are constructed. In this paper two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras of the twelve-dimensional Lie algebra. The reduction of the constructed submodels to invariant submodels of eleven-dimensional and twelve-dimensional Lie algebras is proved.

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ε‎-Invariance

10.1093/oso/9780198821656.003.0006 ◽

2018 ◽

Author(s):

Ercüment H. Ortaçgil

Keyword(s):

Lie Algebra ◽

Lie Group

The discussions up to Chapter 4 have been concerned with the Lie group. In this chapter, the Lie algebra is constructed by defining the operators ∇ and ∇̃.

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Monocular Lie algebra approach for 3D motion estimation

Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004. ◽

10.1109/icpr.2004.1334095 ◽

2004 ◽

Author(s):

J. Ortegon-Aguilar ◽

E. Bayro-Corrochano

Keyword(s):

Motion Estimation ◽

Lie Algebra ◽

3D Motion ◽

Algebra Approach ◽

3D Motion Estimation

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ANTI-SELF-DUAL SOLUTIONS OF THE YANG-MILLS EQUATIONS IN 4n DIMENSIONS

Modern Physics Letters A ◽

10.1142/s0217732392001816 ◽

1992 ◽

Vol 07 (23) ◽

pp. 2077-2085 ◽

Cited By ~ 17

Author(s):

A. D. POPOV

Keyword(s):

Scalar Field ◽

Euclidean Space ◽

Lie Algebra ◽

Linear Equations ◽

Dual Solutions ◽

Gauge Fields ◽

System Of Equations ◽

Semisimple Lie Algebra ◽

Yang Mills ◽

Self Duality

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.

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