Extensions of finite irreducible modules of Lie conformal algebras W(a,b) and some Schrödinger-Virasoro type Lie conformal algebras

Luo, Lipeng; Hong, Yanyong; Wu, Zhixiang

doi:10.1080/00927872.2020.1770779

Cited by 4 publications

(3 citation statements)

References 17 publications

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“…Lie conformal algebra (see [15], β = 0 also see [21]). Here, we note that W(1, 0) and W(2, 0) are respectively Heisenberg-Virasoro Lie conformal algebra and W (2, 2) Lie conformal algebra.…”

Section: Subalgebrasmentioning

confidence: 99%

“…Remark 3.4. The Lie algebra A B(α, β, p) is interesting in the sense that it contains the following subalgebras: (a) when α = p, β = 0, the well-known twisted Heisenberg-Virasoro algebra is isomorphic to the Lie algebra spanned by {L i,0 , W j,0 | i, j ∈ Z}; (b) the Lie algebra generates by {L 0,m , W 0,n | m, n ∈ Z} is isomorphic to the annihilation algebra of W(α ′ , β) in [15].…”

Section: Lemma 33 (1)mentioning

confidence: 99%

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Finite irreducible conformal modules over the extended Block type Lie conformal algebra $\mathfrak{B}(α,β,p)$

Chen,

Hong,

2019

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In this paper, we introduce a class of infinite Lie conformal algebras B(α, β, p), which are the semi-direct sums of Block type Lie conformal algebra B(p) and its non-trivial conformal modules of Zgraded free intermediate series. The annihilation algebras are a class of infinite-dimensional Lie algebras, which include a lot of interesting subalgebras: Virasoro algebra, Block type Lie algebra, twisted Heisenberg-Virasoro algebra and so on. We give a complete classification of all finite non-trivial irreducible conformal modules of B(α, β, p) for α, β ∈ C, p ∈ C * . As an application, the classifications of finite irreducible conformal modules over a series of finite Lie conformal algebras b(n) for n ≥ 1 are given.

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Section: Subalgebrasmentioning

confidence: 99%

Section: Lemma 33 (1)mentioning

confidence: 99%

Finite irreducible conformal modules over the extended Block type Lie conformal algebra $\mathfrak{B}(α,β,p)$

Chen,

Hong,

2019

Preprint

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“…further developed the structure theory [3] and cohomology theory [7] of conformal algebras, and generalized them to pseudoalgebras [4]. Based on Kac's fundamental works, a lot of related researchs have emerged [6,15,19]. In this article, we establish the structure and cohomology theory of n-Lie conformal algebras which are an amalgamation of n-Lie algebras and conformal algebras, and reveal the relation of n-Lie conformal algebras and their associated n-Lie algebras.…”

Section: Introductionmentioning

confidence: 99%

$n$-Lie conformal algebras and its associated infinite-dimensional $n$-Lie algebras

Wang¹,

Luo²,

Wu³

2022

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In this paper, we introduce a {λ1→n−1}-bracket and a distribution notion of an n-Lie conformal algebra. For any n-Lie conformal algebra R, there exists a series of associated infinite-dimensional linearly compact n-Lie algebras {(L iep R) } (p≥1) . We show that torsionless finite n-Lie conformal algebras R and S are isomorphic if and only if (L iep R) ≃ (L iep S) as linearly compact n-Lie algebras with ∂t i -action for any p ≥ 1. Moreover, the representation and cohomology theory of n-Lie conformal algebras are established. In particular, the complex of R is isomorphic to a subcomplex of n-Lie algebra (L iep R) .

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Compatible left-symmetric conformal algebras on W(a, b)

Hong

2022

Communications in Algebra

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Extensions of finite irreducible modules of Lie conformal algebras W(a,b) and some Schrödinger-Virasoro type Lie conformal algebras

Cited by 4 publications

References 17 publications

Finite irreducible conformal modules over the extended Block type Lie conformal algebra $\mathfrak{B}(α,β,p)$

Finite irreducible conformal modules over the extended Block type Lie conformal algebra $\mathfrak{B}(α,β,p)$

$n$-Lie conformal algebras and its associated infinite-dimensional $n$-Lie algebras

Compatible left-symmetric conformal algebras on W(a, b)

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