scholarly journals Biderivations of the higher rank Witt algebra without anti-symmetric condition

2018 ◽  
Vol 16 (1) ◽  
pp. 447-452 ◽  
Author(s):  
Xiaomin Tang ◽  
Yu Yang
Keyword(s):  
Lie Algebra ◽  
Laurent Polynomial ◽  
Low Rank ◽  
Witt Algebra ◽  
Polynomial Algebras ◽  
Derivation Algebra ◽  
Higher Rank

AbstractThe Witt algebra 𝔚d of rank d(≥ 1) is the derivation algebra of Laurent polynomial algebras in d commuting variables. In this paper, all biderivations of 𝔚d without anti-symmetric condition are determined. As an applications, commutative post-Lie algebra structures on 𝔚d are obtained. Our conclusions recover and generalize results in the related papers on low rank or anti-symmetric cases.

Derivations and Automorphism Group of Original Deformative Schrödinger-Virasoro Algebra

2015 ◽  
Vol 22 (03) ◽  
pp. 517-540 ◽  
Author(s):  
Qifen Jiang ◽  
Song Wang
Keyword(s):  
Automorphism Group ◽  
Lie Algebra ◽  
Direct Product ◽  
Virasoro Algebra ◽  
Witt Algebra ◽  
Tensor Density ◽  
Derivation Algebra

In this paper, we determine the derivation algebra and the automorphism group of the original deformative Schrödinger-Virasoro algebra, which is the semi-direct product Lie algebra of the Witt algebra and its tensor density module Ig(a,b).

scholarly journals The Derivation Algebra of Lie Algebra Der(Cq)∝Cq

2015 ◽  
Vol 05 (01) ◽  
pp. 1-7
Author(s):  
志龙 张
Keyword(s):  
Lie Algebra ◽  
Derivation Algebra

Derivations and Automorphism Group of Completed Witt Lie Algebra

2012 ◽  
Vol 19 (03) ◽  
pp. 581-590 ◽  
Author(s):  
Yongping Wu ◽  
Ying Xu ◽  
Lamei Yuan
Keyword(s):  
Finite Element ◽  
Automorphism Group ◽  
Lie Algebra ◽  
Cohomology Group ◽  
Locally Finite ◽  
Simple Lie Algebra ◽  
Derivation Algebra ◽  
First Cohomology Group

In this paper, a simple Lie algebra, referred to as the completed Witt Lie algebra, is introduced. Its derivation algebra and automorphism group are completely described. As a by-product, it is obtained that the first cohomology group of this Lie algebra with coefficients in its adjoint module is trivial. Furthermore, we completely determine the conjugate classes of this Lie algebra under its automorphism group, and also obtain that this Lie algebra does not contain any nonzero ad -locally finite element.

Aggressive Behaviour Between Territorial Cichlids (Astatotilapia Burtoni) in Relation To Rank and Territorial Stability

Behaviour ◽  
1987 ◽  
Vol 103 (4) ◽  
pp. 241-258 ◽  
Author(s):  
Anders Fernö
Keyword(s):  
Sexual Activity ◽  
Physical Aggression ◽  
Aggressive Behaviour ◽  
Low Rank ◽  
Low Level ◽  
Low Intensity ◽  
Boundary Disputes ◽  
Astatotilapia Burtoni ◽  
Higher Rank ◽  
Strong Competition

AbstractTerritorial mosaics of A. burtoni were studied in the laboratory. A difference in rank between neighbouring territorial fish was usually found, with the male with higher rank exhibiting more offensive behaviour and the opponent resisting more passively. A role asymmetry in boundary disputes was found in both high- and low-intensity aggression. Linear rank orders were formed. High rank was associated with a high aggressive and sexual activity towards non-territorial fish and a high mating succes". Territorial size was larger in superior males. A superior did not, however, generally expand his territory towards an inferior. This could be due to the involvement of escalated aggression with the reduction of territory. Most males of low rank did, however, eventually lose their territories. Establishing and losing territories were correlated with a low level of low-intensity aggression. Escalated fighting seldom occurred in spite of a strong competition for females, and aggression was usually limited to Frontal display and low-intensity aggression. Frontal display also played a key role for de-escalation of physical aggression. A. burtoni seems to follow the strategy "Honest", using a honestly graded display with few escalations.

Vertex-algebraic structure of principal subspaces of standard $A^{(2)}_2$-modules, I

2014 ◽  
Vol 25 (07) ◽  
pp. 1450063 ◽  
Author(s):  
C. Calinescu ◽  
J. Lepowsky ◽  
A. Milas
Keyword(s):  
Lie Algebra ◽  
Algebraic Structure ◽  
Test Case ◽  
Basic Formula ◽  
Affine Lie Algebra ◽  
Higher Rank

Extending earlier work of the authors, this is the first in a series of papers devoted to the vertex-algebraic structure of principal subspaces of standard modules for twisted affine Kac–Moody algebras. In this part, we develop the necessary theory of principal subspaces for the affine Lie algebra [Formula: see text], which we expect can be extended to higher rank algebras. As a "test case", we consider the principal subspace of the basic [Formula: see text]-module and explore its structure in depth.

Biological Anaerobic Treatment for Low-Rank Coal Preparation

2011 ◽  
Vol 361-363 ◽  
pp. 328-331
Author(s):  
Li Mei Sun ◽  
Jiang Wu
Keyword(s):  
Biological Treatment ◽  
Culture Medium ◽  
Flow Reactor ◽  
Coal Ash ◽  
Anaerobic Treatment ◽  
Low Rank ◽  
Low Rank Coal ◽  
Higher Rank ◽  
Iron Manganese ◽  
Low Rank Coals

The effect of microbiological treatment of low-rank coal with an anaerobic microbial consortium on theirs characteristics and composition has been inwestigated. A large amount of pyrite sulfur is removed and coal ash is decreased with anaerobic conditions in closed flask. After biological treatment of these low-rank coals in a continuously operationg flow reactor without air blowiong and with everyday aeration, coal ash reduction is found to be more significant under conditions of reactor aeration due to activation of facultative microorganisems. In some time, some metals are removed from two kinds of low-rank coals, includiing iron, manganese, potassium, lithium, toxic and trace metals. The exchange of elements between coal and mineral culture medium depends on coal rank. Metal leaching is higher for higher rank coal.

scholarly journals Higher rank numerical ranges and low rank perturbations of quantum channels

2008 ◽  
Vol 348 (2) ◽  
pp. 843-855 ◽  
Author(s):  
Chi-Kwong Li ◽  
Yiu-Tung Poon ◽  
Nung-Sing Sze
Keyword(s):  
Low Rank ◽  
Quantum Channels ◽  
Higher Rank

scholarly journals Twisted Vertex Operators and Unitary Lie Algebras

2015 ◽  
Vol 67 (3) ◽  
pp. 573-596 ◽  
Author(s):  
Fulin Chen ◽  
Yun Gao ◽  
Naihuan Jing ◽  
Shaobin Tan
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Polynomial Ring ◽  
Central Extension ◽  
Laurent Polynomial ◽  
New Method ◽  
Vertex Operators ◽  
Irreducible Decomposition ◽  
Laurent Polynomial Ring

AbstractA representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral ℤ2–lattice. The irreducible decomposition of the representation is explicitly computed and described. As a by–product, some fundamental representations of affine Kac–Moody Lie algebra of type A(2)n are recovered by the new method.

scholarly journals Note on Generalized Witt Algebras

1959 ◽  
Vol 11 ◽  
pp. 345-352 ◽  
Author(s):  
Rimhak Ree
Keyword(s):  
Lie Algebra ◽  
Additive Group ◽  
Multiplication Table ◽  
Witt Algebra ◽  
Simple Lie Algebra ◽  
Image Position

Throughout this note K will denote a field of characteristic p > 0. Let I be the set {1,2, … , m}, and a finite additive group of functions on I with values in K. We assume that is total in the sense that, for any λ1, … , λm in K Σi=imλiσ(i) = 0 for all a in G implies all σi = 0. It is clear that is an elementary p-group. Let pn be the order of . A generalized Witt algebra is defined as an algebra over K with basis elements {e(σ, i)∣ σ ∈ , i ∈ I} and the multiplication table is a simple Lie algebra except when p = 2, m = 1.

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