Representations of the Local Area-Preserving Lie Algebra for the Klein Bottle

2014 ◽  
Vol 42 (6) ◽  
pp. 2354-2367
Author(s):  
Jingjing Jiang ◽  
Qifen Jiang
Keyword(s):  
Lie Algebra ◽  
Klein Bottle ◽  
Local Area ◽  
Area Preserving

The q-Analog Klein Bottle Lie Algebra

2014 ◽  
Vol 21 (04) ◽  
pp. 561-574
Author(s):  
Cuipo Jiang ◽  
Jingjing Jiang ◽  
Yufeng Pei
Keyword(s):  
Lie Algebra ◽  
Bilinear Form ◽  
Central Extension ◽  
Klein Bottle ◽  
Universal Central Extension ◽  
Finitely Generated ◽  
Invariant Bilinear Form ◽  
Infinite Dimensional ◽  
Simple Lie Algebra ◽  
Infinite Dimensional Lie Algebra

In this paper, we study an infinite-dimensional Lie algebra ℬq, called the q-analog Klein bottle Lie algebra. We show that ℬq is a finitely generated simple Lie algebra with a unique (up to scalars) symmetric invariant bilinear form. The derivation algebra and the universal central extension of ℬq are also determined.

scholarly journals A non-local area preserving curve flow

2013 ◽  
Vol 171 (1) ◽  
pp. 231-247 ◽  
Author(s):  
Li Ma ◽  
Liang Cheng
Keyword(s):  
Local Area ◽  
Curve Flow ◽  
Non Local ◽  
Area Preserving

q-Area Preserving Algebras SDiff(Tk) and the Matrix Algebra $\bar a_{\infty}$

1997 ◽  
Vol 12 (12) ◽  
pp. 821-825 ◽  
Author(s):  
E. H. El Kinani ◽  
M. Zakkari
Keyword(s):  
Lie Algebra ◽  
Matrix Algebra ◽  
Infinite Matrix ◽  
The Matrix ◽  
Area Preserving ◽  
Infinite Set

We consider the infinite matrix Lie algebra [Formula: see text] and an infinite set of its subalgebras parametrized by an Nth root of the unity; qN=1. We obtain the embedding in [Formula: see text] of the area preserving diffeomorphism on the 2-D torus and also its one-parameter deformed version. The correspondence between the area preserving diffeomorphism on the torus Tk, k>2 and the algebra [Formula: see text] is pointed out.

AN AREA-PRESERVING FLOW FOR CLOSED CONVEX PLANE CURVES

2013 ◽  
Vol 24 (04) ◽  
pp. 1350029 ◽  
Author(s):  
YUEYUE MAO ◽  
SHENGLIANG PAN ◽  
YILING WANG
Keyword(s):  
Evolution Equation ◽  
American Mathematical Society ◽  
Nonlinear Problems ◽  
Local Area ◽  
Mathematical Society ◽  
Plane Curves ◽  
Curve Flow ◽  
Convex Plane ◽  
Non Local ◽  
Area Preserving

Motivated by Gage [On an area-preserving evolution equation for plane curves, in Nonlinear Problems in Geometry, ed. D. M. DeTurck, Contemporary Mathematics, Vol. 51 (American Mathematical Society, Providence, RI, 1986), pp. 51–62] and Ma–Cheng [A non-local area preserving curve flow, preprint (2009), arXiv:0907.1430v2, [math.DG]], in this paper, an area-preserving flow for convex plane curves is presented. This flow will decrease the perimeter of the evolving curve and make the curve more and more circular during the evolution process. And finally, as t goes to infinity, the limiting curve will be a finite circle in the C∞ metric.

scholarly journals Jet modules for the centerless Virasoro-like algebra

2019 ◽  
Vol 18 (01) ◽  
pp. 1950002 ◽  
Author(s):  
Xiangqian Guo ◽  
Genqiang Liu
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Block Type ◽  
Simple Lie Algebras ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Irreducible Modules ◽  
Infinite Dimensional Lie Algebra ◽  
Area Preserving

In this paper, we studied the jet modules for the centerless Virasoro-like algebra which is the Lie algebra of the Lie group of the area-preserving diffeomorphisms of a [Formula: see text]-torus. The jet modules are certain natural modules over the Lie algebra of semi-direct product of the centerless Virasoro-like algebra and the Laurent polynomial algebra in two variables. We reduce the irreducible jet modules to the finite-dimensional irreducible modules over some infinite-dimensional Lie algebra and then characterize the irreducible jet modules with irreducible finite dimensional modules over [Formula: see text]. To determine the indecomposable jet modules, we use the technique of polynomial modules in the sense of [Irreducible representations for toroidal Lie algebras, J. Algebras 221 (1999) 188–231; Weight modules over exp-polynomial Lie algebras, J. Pure Appl. Algebra 191 (2004) 23–42]. Consequently, indecomposable jet modules are described using modules over the algebra [Formula: see text], which is the “positive part” of a Block type algebra studied first by [Some infinite-dimensional simple Lie algebras in characteristic [Formula: see text] related to those of Block, J. Pure Appl. Algebra 127(2) (1998) 153–165] and recently by [A [Formula: see text]-graded generalization of the Witt-algebra, preprint; Classification of simple Lie algebras on a lattice, Proc. London Math. Soc. 106(3) (2013) 508–564]).

Strathnet—a local area network

1981 ◽  
Vol 1 (1) ◽  
pp. 21 ◽  
Author(s):  
David Hutchison ◽  
Doug Shepherd
Keyword(s):  
Local Area Network ◽  
Local Area ◽  
Area Network
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