Inversion of Finite ToeplitzMatrices Consisting of Elements of a Noncommutative Algebra

2010 ◽  
pp. 7-46 ◽  
Author(s):  
Israel Gohberg ◽  
Georg Heinig
Keyword(s):  
Noncommutative Algebra

Interactions between Algebraic Geometry and Noncommutative Algebra

2006 ◽  
pp. 1319-1384
Author(s):  
Dieter Happel ◽  
Lance Small ◽  
J. Stafford ◽  
Michel Van den Bergh
Keyword(s):  
Algebraic Geometry ◽  
Noncommutative Algebra

scholarly journals Introduce of Generalized Uncertainty Principle

2014 ◽  
Vol 39 ◽  
pp. 10-20
Author(s):  
Seyed Davood Sadatian
Keyword(s):  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Noncommutative Algebra

We study and explain the uncertainty principle. We've discussed how to reform the uncertainty principle. In this regards, we have used the mechanisms of noncommutative algebra for obtain a generalized uncertainty principle. Following, Due to modified relationship uncertainty, we consider some application of these relation

scholarly journals Composite system in rotationally invariant noncommutative phase space

2018 ◽  
Vol 33 (07) ◽  
pp. 1850037 ◽  
Author(s):  
Kh. P. Gnatenko ◽  
V. M. Tkachuk
Keyword(s):  
Phase Space ◽  
Composite System ◽  
Particle System ◽  
Rotational Symmetry ◽  
Center Of Mass ◽  
Noncommutative Space ◽  
Effective Parameters ◽  
Noncommutative Phase Space ◽  
Noncommutative Algebra ◽  
Rotationally Invariant

Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of composite system reproduce noncommutative algebra for coordinates and momenta of individual particles. Also, on these conditions, the coordinates and the momenta of the center-of-mass satisfy noncommutative algebra with effective parameters of noncommutativity which depend on the total mass of the system and do not depend on its composition. Besides, it is shown that on these conditions the coordinates in noncommutative space do not depend on mass and can be considered as kinematic variables, the momenta are proportional to mass as it has to be. A two-particle system with Coulomb interaction is studied and the corrections to the energy levels of the system are found in rotationally invariant noncommutative phase space. On the basis of this result the effect of noncommutativity on the spectrum of exotic atoms is analyzed.

One-Dimensional Representations of the Cycle Subalgebra of a Semi-Simple Lie Algebra

1970 ◽  
Vol 13 (4) ◽  
pp. 463-467 ◽  
Author(s):  
F. W. Lemire
Keyword(s):  
Lie Algebra ◽  
Cartan Subalgebra ◽  
Mass Function ◽  
Algebra Homomorphism ◽  
Closed Field ◽  
Noncommutative Algebra ◽  
One Dimensional ◽  
Finite Dimensional ◽  
The Difference ◽  
Mass Functions

Let L denote a semi-simple, finite dimensional Lie algebra over an algebraically closed field K of characteristic zero. If denotes a Cartan subalgebra of L and denotes the centralizer of in the universal enveloping algebra U of L, then it has been shown that each algebra homomorphism (called a "mass-function" on ) uniquely determines a linear irreducible representation of L. The technique involved in this construction is analogous to the Harish-Chandra construction [2] of dominated irreducible representations of L starting from a linear functional . The difference between the two results lies in the fact that all linear functionals on are readily obtained, whereas since is in general a noncommutative algebra the construction of mass-functions is decidedly nontrivial.

A simple example of a noncommutative algebra

1959 ◽  
Vol 52 (7) ◽  
pp. 534-540
Author(s):  
Arnold Wendt
Keyword(s):  
Noncommutative Algebra

Students may not consider the commutative principle very important if they never see an example where multiplication is noncommutative.

scholarly journals SCALING OF VARIABLES AND THE RELATION BETWEEN NONCOMMUTATIVE PARAMETERS IN NONCOMMUTATIVE QUANTUM MECHANICS

2006 ◽  
Vol 21 (10) ◽  
pp. 795-802 ◽  
Author(s):  
O. BERTOLAMI ◽  
J. G. ROSA ◽  
C. M. L. DE ARAGÃO ◽  
P. CASTORINA ◽  
D. ZAPPALÀ
Keyword(s):  
Quantum Mechanics ◽  
The Self ◽  
Effective Parameters ◽  
Noncommutative Algebra ◽  
Noncommutative Quantum Mechanics ◽  
Self Consistent ◽  
Limited Applicability ◽  
Direct Proportionality ◽  
Space Noncommutativity ◽  
Noncommutative Quantum

We consider noncommutative quantum mechanics with phase space noncommutativity. In particular, we show that a scaling of variables leaves the noncommutative algebra invariant, so that only the self-consistent effective parameters of the model are physically relevant. We also discuss the recently proposed relation of direct proportionality between the noncommutative parameters, showing that it has a limited applicability.

scholarly journals INTRODUCTION

2013 ◽  
Vol 55 (A) ◽  
pp. 1-2
Author(s):  
IAIN GORDON ◽  
ULRICH KRÄHMER ◽  
TOM LENAGAN ◽  
DAN ROGALSKI
Keyword(s):  
Noncommutative Algebra ◽  
New Developments ◽  
The World ◽  
Isle Of Skye

This issue is the proceedings of a conference “New Developments in Noncommutative Algebra and its Applications” held to celebrate the 60th birthdays of Kenny Brown and Toby Stafford, at Sabhal Mòr Ostaig on the Isle of Skye in June 2011. The papers in this issue, by some of the leading noncommutative algebraists in the world, represent several of the topics in which Kenny and Toby work.

scholarly journals Effect of noncommutativity on the spectrum of free particle and harmonic oscillator in rotationally invariant noncommutative phase space

2018 ◽  
Vol 33 (16) ◽  
pp. 1850091 ◽  
Author(s):  
Kh. P. Gnatenko ◽  
O. V. Shyiko
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Rotational Symmetry ◽  
Free Particle ◽  
Second Order ◽  
Noncommutative Phase Space ◽  
Noncommutative Algebra ◽  
Ordinary Space ◽  
Canonical Type ◽  
Rotationally Invariant

We consider rotationally invariant noncommutative algebra with tensors of noncommutativity constructed with the help of additional coordinates and momenta. The algebra is equivalent to the well-known noncommutative algebra of canonical type. In the noncommutative phase space, rotational symmetry influence of noncommutativity on the spectrum of free particle and the spectrum of harmonic oscillator is studied up to the second-order in the parameters of noncommutativity. We find that because of momentum noncommutativity, the spectrum of free particle is discrete and corresponds to the spectrum of harmonic oscillator in the ordinary space (space with commutative coordinates and commutative momenta). We obtain the spectrum of the harmonic oscillator in the rotationally invariant noncommutative phase space and conclude that noncommutativity of coordinates affects its mass. The frequency of the oscillator is affected by the coordinate noncommutativity and the momentum noncommutativity. On the basis of the results, the eigenvalues of squared length operator are found and restrictions on the value of length in noncommutative phase space with rotational symmetry are analyzed.

scholarly journals Noncommutative Effects on the Fluid Dynamics and Modifications of the Friedmann Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Kai Ma
Keyword(s):  
Fluid Dynamics ◽  
Poisson Bracket ◽  
Mass Density ◽  
Equations Of Motion ◽  
Friedmann Equation ◽  
Noncommutative Space ◽  
Lagrangian Formalism ◽  
Noncommutative Algebra ◽  
Symmetry Properties ◽  
Lagrangian Variables

We propose a new approach in Lagrangian formalism for studying the fluid dynamics on noncommutative space. Starting with the Poisson bracket for single particle, a map from canonical Lagrangian variables to Eulerian variables is constructed for taking into account the noncommutative effects. The advantage of this approach is that the kinematic and potential energies in the Lagrangian formalism continuously change in the infinite limit to the ones in Eulerian formalism and hence make sure that both the kinematical and potential energies are taken into account correctly. Furthermore, in our approach, the equations of motion of the mass density and current density are naturally expressed into conservative form. Based on this approach, the noncommutative Poisson bracket is introduced, and the noncommutative algebra among Eulerian variables and the noncommutative corrections on the equations of motion are obtained. We find that the noncommutative corrections generally depend on the derivatives of potential under consideration. Furthermore, we find that the noncommutative algebra does modify the usual Friedmann equation, and the noncommutative corrections measure the symmetry properties of the density function ρ(z→) under rotation around the direction θ→. This characterization results in vanishing corrections for spherically symmetric mass density distribution and potential.

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