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 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 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.

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

Finite irreducible representations of map Lie conformal algebras

2017 ◽  
Vol 28 (01) ◽  
pp. 1750002 ◽  
Author(s):  
Henan Wu
Keyword(s):  
Representation Theory ◽  
Associative Algebra ◽  
Complete Classification ◽  
Conformal Algebra ◽  
Irreducible Representations ◽  
Finite Representation ◽  
Finite Dimensional ◽  
Conformal Algebras ◽  
Commutative Associative Algebra

In this paper, we study the finite representation theory of the map Lie conformal algebra [Formula: see text], where G is a finite simple Lie conformal algebra and A is a commutative associative algebra with unity over [Formula: see text]. In particular, we give a complete classification of nontrivial finite irreducible conformal modules of [Formula: see text] provided A is finite-dimensional.

Note on the spectral classification of carbon stars in the photographic infrared region

1966 ◽  
Vol 24 ◽  
pp. 21-23
Author(s):  
Y. Fujita
Keyword(s):  
Infrared Region ◽  
Spectral Classification ◽  
Carbon Stars

We have investigated the spectrograms (dispersion: 8Å/mm) in the photographic infrared region fromλ7500 toλ9000 of some carbon stars obtained by the coudé spectrograph of the 74-inch reflector attached to the Okayama Astrophysical Observatory. The names of the stars investigated are listed in Table 1.

Diagnostic Value of Electron Microscopy in Soft Tissue Tumors

1970 ◽  
Vol 28 ◽  
pp. 220-221
Author(s):  
Gerald Fine ◽  
Azorides R. Morales
Keyword(s):  
Cardiac Myxoma ◽  
Osteogenic Sarcoma ◽  
Diagnostic Value ◽  
Soft Tissue Tumors ◽  
Amelanotic Melanoma ◽  
Growth Patterns ◽  
Light Microscopic Level ◽  
Mesenchymal Tumors ◽  
Good Agreement

For years the separation of carcinoma and sarcoma and the subclassification of sarcomas has been based on the appearance of the tumor cells and their microscopic growth pattern and information derived from certain histochemical and special stains. Although this method of study has produced good agreement among pathologists in the separation of carcinoma from sarcoma, it has given less uniform results in the subclassification of sarcomas. There remain examples of neoplasms of different histogenesis, the classification of which is questionable because of similar cytologic and growth patterns at the light microscopic level; i.e. amelanotic melanoma versus carcinoma and occasionally sarcoma, sarcomas with an epithelial pattern of growth simulating carcinoma, histologically similar mesenchymal tumors of different histogenesis (histiocytoma versus rhabdomyosarcoma, lytic osteogenic sarcoma versus rhabdomyosarcoma), and myxomatous mesenchymal tumors of diverse histogenesis (myxoid rhabdo and liposarcomas, cardiac myxoma, myxoid neurofibroma, etc.)

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