Structure of a Class of Rank Two Lie Conformal Algebras

2021 ◽  
Vol 28 (01) ◽  
pp. 169-180
Author(s):  
Wei Wang ◽  
Chunguang Xia
Keyword(s):  
Complex Number ◽  
Central Extensions ◽  
Conformal Algebras ◽  
Rank One

Let [Formula: see text] be a complex number, and a class of non-semisimple and non-solvable rank two Lie conformal algebras [Formula: see text] are introduced. In this paper, conformal derivations, conformal quasiderivations, generalized conformal derivations and conformal biderivations of [Formula: see text] are studied. Besides, central extensions and conformal modules of rank one of [Formula: see text] are determined.

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.

Lie conformal algebras related to Galilean conformal algebras

2020 ◽  
pp. 2150075
Author(s):  
Xiu Han ◽  
Dengyin Wang ◽  
Chunguang Xia
Keyword(s):  
Conformal Algebra ◽  
Complex Numbers ◽  
Conformal Algebras ◽  
Rank One ◽  
Intermediate Series

Let [Formula: see text] be a Lie conformal algebra related to Galilean conformal algebras, where [Formula: see text] are complex numbers. All the conformal derivations of [Formula: see text] are shown to be inner. The rank one conformal modules and [Formula: see text]-graded free intermediate series modules over [Formula: see text] are completely classified. The corresponding results of the finite conformal subalgebra of [Formula: see text] are also obtained as byproducts.

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.

scholarly journals Finite irreducible conformal modules of rank two Lie conformal algebras

2020 ◽  
pp. 2150145
Author(s):  
Maosen Xu ◽  
Yanyong Hong ◽  
Zhixiang Wu
Keyword(s):  
Irreducible Module ◽  
Conformal Algebra ◽  
Conformal Algebras ◽  
Irreducible Modules ◽  
Rank One

In the present paper, we prove that any finite nontrivial irreducible module over a rank two Lie conformal algebra [Formula: see text] is of rank one. We also describe the actions of [Formula: see text] on its finite irreducible modules explicitly. Moreover, we show that all finite nontrivial irreducible modules of finite Lie conformal algebras whose semisimple quotient is the Virasoro Lie conformal algebra are of rank one.

scholarly journals Quadratic Leibniz conformal algebras

2019 ◽  
Vol 18 (10) ◽  
pp. 1950195
Author(s):  
Jinsen Zhou ◽  
Yanyong Hong
Keyword(s):  
Conformal Algebra ◽  
Bilinear Forms ◽  
Central Extensions ◽  
One Dimensional ◽  
Conformal Algebras ◽  
Equivalent Characterization ◽  
Algebraic Operations

In this paper, we study a class of Leibniz conformal algebras called quadratic Leibniz conformal algebras. An equivalent characterization of a Leibniz conformal algebra [Formula: see text] through three algebraic operations on [Formula: see text] is given. By this characterization, several constructions of quadratic Leibniz conformal algebras are presented. Moreover, one-dimensional central extensions of quadratic Leibniz conformal algebras are considered using some bilinear forms on [Formula: see text]. In particular, we also study one-dimensional Leibniz central extensions of quadratic Lie conformal algebras.

scholarly journals Loop W(a,b) Lie conformal algebra

2016 ◽  
Vol 27 (02) ◽  
pp. 1650016 ◽  
Author(s):  
Guangzhe Fan ◽  
Henan Wu ◽  
Bo Yu
Keyword(s):  
Lie Algebra ◽  
Conformal Algebra ◽  
Central Extensions ◽  
Rank One ◽  
Formal Distribution

Fix [Formula: see text], let [Formula: see text] be the loop [Formula: see text] Lie algebra over [Formula: see text] with basis [Formula: see text] and relations [Formula: see text], where [Formula: see text]. In this paper, a formal distribution Lie algebra of [Formula: see text] is constructed. Then the associated conformal algebra [Formula: see text] is studied, where [Formula: see text] has a [Formula: see text]-basis [Formula: see text] with [Formula: see text]-brackets [Formula: see text] and [Formula: see text]. In particular, we determine the conformal derivations and rank one conformal modules of this conformal algebra. Finally, we study the central extensions and extensions of conformal modules.

Extensions of modules over a class of Lie conformal algebras 𝒲(b)

2019 ◽  
Vol 18 (09) ◽  
pp. 1950164 ◽  
Author(s):  
Kaijing Ling ◽  
Lamei Yuan
Keyword(s):  
Complex Number ◽  
Conformal Algebras ◽  
Nonzero Complex Number

Let [Formula: see text] be a class of free Lie conformal algebras of rank two with [Formula: see text]-basis [Formula: see text] and relations [Formula: see text] where [Formula: see text] is a nonzero complex number. In this paper, we classify extensions between two finite irreducible conformal modules over the Lie conformal algebras [Formula: see text].

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