Classification of maximal subalgebras of rank n of the conformal algebra AC(1, n)

1998 ◽  
Vol 50 (4) ◽  
pp. 519-532 ◽  
Author(s):  
A. F. Barannik ◽  
I. I. Yurik
Keyword(s):  
Conformal Algebra ◽  
Maximal Subalgebras

scholarly journals Symmetry analysis of the Klein–Gordon equation in Bianchi I spacetimes

2015 ◽  
Vol 12 (03) ◽  
pp. 1550033 ◽  
Author(s):  
A. Paliathanasis ◽  
M. Tsamparlis ◽  
M. T. Mustafa
Keyword(s):  
Wave Equation ◽  
Gordon Equation ◽  
Invariant Solution ◽  
Lie Symmetries ◽  
Conformal Algebra ◽  
Noether Symmetries ◽  
Bianchi I ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this work we perform the symmetry classification of the Klein–Gordon equation in Bianchi I spacetime. We apply a geometric method which relates the Lie symmetries of the Klein–Gordon equation with the conformal algebra of the underlying geometry. Furthermore, we prove that the Lie symmetries which follow from the conformal algebra are also Noether symmetries for the Klein–Gordon equation. We use these results in order to determine all the potentials in which the Klein–Gordon admits Lie and Noether symmetries. Due to the large number of cases and for easy reference the results are presented in the form of tables. For some of the potentials we use the Lie admitted symmetries to determine the corresponding invariant solution of the Klein–Gordon equation. Finally, we show that the results also solve the problem of classification of Lie/Noether point symmetries of the wave equation in Bianchi I spacetime and can be used for the determination of invariant solutions of the wave equation.

Finite irreducible modules of Lie conformal algebras 𝒲(a,b) and some Schrödinger–Virasoro type Lie conformal algebras

2019 ◽  
Vol 30 (06) ◽  
pp. 1950026 ◽  
Author(s):  
Lipeng Luo ◽  
Yanyong Hong ◽  
Zhixiang Wu
Keyword(s):  
Complete Classification ◽  
Conformal Algebra ◽  
Direct Sums ◽  
Conformal Algebras ◽  
Irreducible Modules ◽  
Rank One ◽  
Virasoro Type

Lie conformal algebras [Formula: see text] are the semi-direct sums of Virasoro Lie conformal algebra and its nontrivial conformal modules of rank one. In this paper, we first give a complete classification of all finite nontrivial irreducible conformal modules of [Formula: see text]. It is shown that all such modules are of rank one. Moreover, with a similar method, all finite nontrivial irreducible conformal modules of Schrödinger–Virasoro type Lie conformal algebras [Formula: see text] and [Formula: see text] are characterized.

Classification of compatible left-symmetric conformal algebraic structures on the Lie conformal algebra W(a,b)

2018 ◽  
Vol 46 (12) ◽  
pp. 5381-5398
Author(s):  
Deng Liu ◽  
Yanyong Hong ◽  
Hao Zhou ◽  
Nuan Zhang
Keyword(s):  
Conformal Algebra ◽  
Algebraic Structures

scholarly journals Classification of finite irreducible conformal modules over Lie conformal algebra \mathcal{W}(a, b, r)

2020 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Wenjun Liu ◽  
◽  
Yukun Xiao ◽  
Xiaoqing Yue
Keyword(s):  
Conformal Algebra

scholarly journals The Lie Conformal Algebra of a Block Type Lie Algebra

2015 ◽  
Vol 22 (03) ◽  
pp. 367-382 ◽  
Author(s):  
Ming Gao ◽  
Ying Xu ◽  
Xiaoqing Yue
Keyword(s):  
Lie Algebra ◽  
Conformal Algebra ◽  
Block Type ◽  
Intermediate Series ◽  
Formal Distribution

Let L be a Lie algebra of Block type over ℂ with basis {Lα,i | α,i ∈ ℤ} and brackets [Lα,i,Lβ,j]=(β(i+1)-α(j+1)) Lα+β,i+j. In this paper, we first construct a formal distribution Lie algebra of L. Then we decide its conformal algebra B with ℂ[∂]-basis {Lα(w) | α ∈ ℤ} and λ-brackets [Lα(w)λ Lβ(w)]= (α∂+(α+β)λ) Lα+β(w). Finally, we give a classification of free intermediate series B-modules.

scholarly journals Maximal subalgebras for Lie superalgebras of Cartan type

2014 ◽  
Vol 14 (02) ◽  
pp. 1550013 ◽  
Author(s):  
Wei Bai ◽  
Wende Liu ◽  
Xuan Liu ◽  
Hayk Melikyan
Keyword(s):  
Lie Superalgebras ◽  
Constructive Method ◽  
Prime Characteristic ◽  
Maximal Subalgebras ◽  
Cartan Type ◽  
Isomorphism Classes

The maximal graded subalgebras for four families of Lie superalgebras of Cartan type over a field of prime characteristic are studied. All maximal graded subalgebras are described completely by a constructive method and their isomorphism classes, dimension formulas are found except for maximal irreducible graded subalgebras. The classification of maximal irreducible graded subalgebras is reduced to the classification of the maximal irreducible subalgebras for the classical Lie superalgebras 𝔤𝔩(m, n), 𝔰𝔩(m, n) and 𝔬𝔰𝔭(m, n).

On the classification of subalgebras of the conformal algebra with respect to inner automorphisms

1998 ◽  
Vol 39 (9) ◽  
pp. 4899-4922 ◽  
Author(s):  
L. F. Barannyk ◽  
P. Basarab-Horwath ◽  
W. I. Fushchych
Keyword(s):  
Conformal Algebra ◽  
Inner Automorphisms
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