scholarly journals Another Representation for the Maximal Lie Algebra ofsl(n+2,ℝ)in Terms of Operators

2009 ◽  
Vol 2009 ◽  
pp. 1-3
Author(s):  
Tooba Feroze ◽  
Asghar Qadir
Keyword(s):  
Differential Equations ◽  
Lie Algebra ◽  
Linear Group ◽  
Symmetry Algebra ◽  
Special Linear Group ◽  
Real Numbers ◽  
Special Linear ◽  
The Real

We provide an alternate representation to the result that the Lie algebra of generators of the system ofndifferential equations,(ya)″=0, is isomorphic to the Lie algebra of the special linear group of order(n+2), over the real numbers,sl(n+2,ℝ). In this paper, we provide an alternate representation of the symmetry algebra by simple relabelling of indices. This provides one more proof of the result that the symmetry algebra of(ya)″=0issl(n+2,ℝ).

scholarly journals An integrable system of partial differential equations on the special linear group

2002 ◽  
Vol 44 (1) ◽  
pp. 83-93
Author(s):  
Peter J. Vassiliou
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Group ◽  
Special Linear Group ◽  
Partial Differential ◽  
Special Linear ◽  
First Order ◽  
Independent Variables ◽  
Two Independent Variables

AbstractWe give an intrinsic construction of a coupled nonlinear system consisting of two first-order partial differential equations in two dependent and two independent variables which is determined by a hyperbolic structure on the complex special linear group regarded as a real Lie groupG. Despite the fact that the system is not Darboux semi-integrable at first order, the construction of a family of solutions depending.upon two arbitrary functions, each of one variable, is reduced to a system of ordinary differential equations on the 1-jets. The ordinary differential equations in question are of Lie type and associated withG.

scholarly journals Magnetic curves in the real special linear group

2019 ◽  
Vol 23 (8) ◽  
pp. 2161-2205 ◽  
Author(s):  
Jun-Ichi Inoguchi ◽  
Marian Ioan Munteanu
Keyword(s):  
Linear Group ◽  
Special Linear Group ◽  
Special Linear ◽  
The Real

scholarly journals Order Conditions for Sampling the Invariant Measure of Ergodic Stochastic Differential Equations on Manifolds

2021 ◽  
Author(s):  
Adrien Laurent ◽  
Gilles Vilmart
Keyword(s):  
Invariant Measure ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Linear Group ◽  
Langevin Equation ◽  
Numerical Experiments ◽  
Special Linear Group ◽  
Order Conditions ◽  
High Order ◽  
Differential Equations On Manifolds

AbstractWe derive a new methodology for the construction of high-order integrators for sampling the invariant measure of ergodic stochastic differential equations with dynamics constrained on a manifold. We obtain the order conditions for sampling the invariant measure for a class of Runge–Kutta methods applied to the constrained overdamped Langevin equation. The analysis is valid for arbitrarily high order and relies on an extension of the exotic aromatic Butcher-series formalism. To illustrate the methodology, a method of order two is introduced, and numerical experiments on the sphere, the torus and the special linear group confirm the theoretical findings.

scholarly journals Integral cohomology and Chern classes of the special linear group over the ring of integers

2001 ◽  
Vol 131 (3) ◽  
pp. 445-457
Author(s):  
DOMINIQUE ARLETTAZ ◽  
CHRISTIAN AUSONI ◽  
MAMORU MIMURA ◽  
NOBUAKI YAGITA
Keyword(s):  
Linear Group ◽  
Upper Bound ◽  
Special Linear Group ◽  
Discrete Groups ◽  
Chern Classes ◽  
Additive Structure ◽  
Special Linear ◽  
Ring Of Integers ◽  
Integral Cohomology ◽  
Complete Calculation

This paper is devoted to the complete calculation of the additive structure of the 2-torsion of the integral cohomology of the infinite special linear group SL(ℤ) over the ring of integers ℤ. This enables us to determine the best upper bound for the order of the Chern classes of all integral and rational representations of discrete groups.

scholarly journals The third homology of the special linear group of a field

2009 ◽  
Vol 213 (9) ◽  
pp. 1665-1680 ◽  
Author(s):  
Kevin Hutchinson ◽  
Liqun Tao
Keyword(s):  
Linear Group ◽  
Special Linear Group ◽  
Special Linear ◽  
The Third

On the existence of Engel pairs in certain linear groups

2016 ◽  
Vol 15 (04) ◽  
pp. 1650062
Author(s):  
S. G. Quek ◽  
K. B. Wong ◽  
P. C. Wong
Keyword(s):  
Linear Group ◽  
Field Extension ◽  
Special Linear Group ◽  
Linear Groups ◽  
Special Linear

Let [Formula: see text] be a group and [Formula: see text]. The 2-tuple [Formula: see text] is said to be an [Formula: see text]-Engel pair, [Formula: see text], if [Formula: see text], [Formula: see text] and [Formula: see text]. Let SL[Formula: see text] be the special linear group of degree [Formula: see text] over the field [Formula: see text]. In this paper, we show that given any field [Formula: see text], there is a field extension [Formula: see text] of [Formula: see text] with [Formula: see text] such that SL[Formula: see text] has an [Formula: see text]-Engel pair for some integer [Formula: see text]. We will also show that SL[Formula: see text] has a [Formula: see text]-Engel pair if [Formula: see text] is a field of characteristic [Formula: see text].

scholarly journals The special linear group for nonassociative rings

2020 ◽  
Vol 23 (2) ◽  
pp. 327-335
Author(s):  
Harry Petyt
Keyword(s):  
Linear Group ◽  
Special Linear Group ◽  
Large Classes ◽  
Special Linear ◽  
Lie Ring ◽  
Definition Of ◽  
Associative Rings

AbstractWe extend to arbitrary rings a definition of the octonion special linear group due to Baez. At the infinitesimal level, we get a Lie ring, which we describe over some large classes of rings, including all associative rings and all algebras over a field. As a corollary, we compute all the groups Baez defined.

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