scholarly journals Classification of finite irreducible conformal modules over some Lie conformal algebras related to the Virasoro conformal algebra

2017 ◽  
Vol 58 (4) ◽  
pp. 041701 ◽  
Author(s):  
Henan Wu ◽  
Lamei Yuan
Keyword(s):  
Conformal Algebra ◽  
Conformal Algebras

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.

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.

scholarly journals Loop Schrödinger–Virasoro Lie conformal algebra

2016 ◽  
Vol 27 (06) ◽  
pp. 1650057 ◽  
Author(s):  
Haibo Chen ◽  
Jianzhi Han ◽  
Yucai Su ◽  
Ying Xu
Keyword(s):  
Lie Algebra ◽  
Conformal Algebra ◽  
Cohomology Groups ◽  
Conformal Algebras ◽  
Rank One ◽  
Intermediate Series

In this paper, we introduce two kinds of Lie conformal algebras, associated with the loop Schrödinger–Virasoro Lie algebra and the extended loop Schrödinger–Virasoro Lie algebra, respectively. The conformal derivations, the second cohomology groups of these two conformal algebras are completely determined. And nontrivial free conformal modules of rank one and [Formula: see text]-graded free intermediate series modules over these two conformal algebras are also classified in the present paper.

scholarly journals GALILEAN CONFORMAL ALGEBRA IN SEMI-INFINITE SPACE

2012 ◽  
Vol 27 (09) ◽  
pp. 1250044
Author(s):  
M. R. SETARE ◽  
V. KAMALI
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Correlation Functions ◽  
Fixed Time ◽  
Space Time ◽  
Conformal Algebra ◽  
Infinite Space ◽  
Conformal Algebras

In the present paper, we considered Galilean conformal algebras (GCAs), which arises as a contraction relativistic conformal algebras (xi→ϵxi, t→t, ϵ→0). We can use the Galilean conformal (GC) symmetry to constrain two-point and three-point functions. Correlation functions in space–time without boundary condition were found [A. Bagchi and I. Mandal, Phys. Lett. B675, 393 (2009).]. In real situations, there are boundary conditions in space–time, so we have calculated correlation functions for GC invariant fields in semi-infinite space with boundary condition in r = 0. We have calculated two-point and three-point functions with boundary condition in fixed time.

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.

scholarly journals Generalized conformal derivations of Lie conformal algebras

2019 ◽  
Vol 18 (09) ◽  
pp. 1950175
Author(s):  
Guangzhe Fan ◽  
Yanyong Hong ◽  
Yucai Su
Keyword(s):  
Natural Generalization ◽  
Conformal Algebra ◽  
Derivation Algebra ◽  
Conformal Algebras

Let [Formula: see text] be a finite Lie conformal algebra. The purpose of this paper is to investigate the conformal derivation algebra [Formula: see text], the conformal quasiderivation algebra [Formula: see text] and the generalized conformal derivation algebra [Formula: see text]. The generalized conformal derivation algebra is a natural generalization of the conformal derivation algebra. Obviously, we have the following tower [Formula: see text], where [Formula: see text] is the general Lie conformal algebra. Furthermore, we mainly research the connection of these generalized conformal derivations. Finally, the conformal [Formula: see text]-derivations of Lie conformal algebras are studied. Moreover, we obtain some connections between several specific generalized conformal derivations and the conformal [Formula: see text]-derivations. In addition, all conformal [Formula: see text]-derivations of finite simple Lie conformal algebras are characterized.

scholarly journals Subalgebras of gcN and Jacobi Polynomials

2002 ◽  
Vol 45 (4) ◽  
pp. 567-605 ◽  
Author(s):  
Alberto De Sole ◽  
Victor G. Kac
Keyword(s):  
Jacobi Polynomials ◽  
Conformal Algebra ◽  
Conformal Algebras

AbstractWe classify the subalgebras of the general Lie conformal algebra gcN that act irreducibly on [∂]N and that are normalized by the sl2-part of a Virasoro element. The problem turns out to be closely related to classical Jacobi polynomials , σ ∈ . The connection goes both ways—we use in our classification some classical properties of Jacobi polynomials, and we derive from the theory of conformal algebras some apparently new properties of Jacobi polynomials.

scholarly journals Universal enveloping Poisson conformal algebras

2020 ◽  
Vol 30 (05) ◽  
pp. 1015-1034
Author(s):  
P. S. Kolesnikov
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Conformal Algebra ◽  
Vertex Operator Algebras ◽  
Conformal Algebras

Lie conformal algebras are useful tools for studying vertex operator algebras and their representations. In this paper, we establish close relations between Poisson conformal algebras and representations of Lie conformal algebras. We also calculate explicitly Poisson conformal brackets on the associated graded conformal algebras of universal associative conformal envelopes of the Virasoro conformal algebra and the Neveu–Schwartz conformal superalgebra.

scholarly journals A new Composition-Diamond lemma for associative conformal algebras

2017 ◽  
Vol 16 (05) ◽  
pp. 1750094 ◽  
Author(s):  
Lili Ni ◽  
Yuqun Chen
Keyword(s):  
Conformal Algebra ◽  
Ideal Formula ◽  
Linear Basis ◽  
Conformal Algebras ◽  
Normal Formula

Let [Formula: see text] be the free associative conformal algebra generated by a set [Formula: see text] with a bounded locality [Formula: see text]. Let [Formula: see text] be a subset of [Formula: see text]. A Composition-Diamond lemma for associative conformal algebras is first established by Bokut, Fong and Ke in 2004 [L. A. Bokut, Y. Fong and W.-F. Ke, Composition-Diamond Lemma for associative conformal algebras, J. Algebra 272 (2004) 739–774] which claims that if (i) [Formula: see text] is a Gröbner–Shirshov basis in [Formula: see text], then (ii) the set of [Formula: see text]-irreducible words is a linear basis of the quotient conformal algebra [Formula: see text], but not conversely. In this paper, by introducing some new definitions of normal [Formula: see text]-words, compositions and compositions to be trivial, we give a new Composition-Diamond lemma for associative conformal algebras, which makes the conditions (i) and (ii) equivalent. We show that for each ideal [Formula: see text] of [Formula: see text], [Formula: see text] has a unique reduced Gröbner–Shirshov basis. As applications, we show that Loop Virasoro Lie conformal algebra and Loop Heisenberg–Virasoro Lie conformal algebra are embeddable into their universal enveloping associative conformal algebras.

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