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:10.1142/s0129167x19500265

Cited by 10 publications

(2 citation statements)

References 18 publications

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“…Since the Virasoro Lie conformal algebra Vir and Lie conformal algebra W(a, b) are both the subalgebras of W(a, b, r), we recall some results about their modules. From [5,15], we have the following two propositions. Proposition 1.…”

Section: Definition 22 a Conformal Module M Over A Lie Conformal Almentioning

confidence: 99%

“…A more general class of Lie conformal algebras W(a, b), constructed as a semi-direct sum of Virasoro Lie conformal algebra and its nontrivial conformal modules of rank one, was introduced in [14]. A complete classification of finite irreducible conformal modules of W(a, b) was recently given in [15]. W(1, 0) is just the Heisenberg-Virasoro Lie conformal algebra.…”

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Classification of finite irreducible conformal modules over Lie conformal algebra <inline-formula><tex-math id="M1">$ \mathcal{W}(a, b, r) $</tex-math></inline-formula>

Liu

Xiao

Yue

2021

era

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<p style='text-indent:20px;'>We study a family of non-simple Lie conformal algebras <inline-formula><tex-math id="M2">$ \mathcal{W}(a,b,r) $</tex-math></inline-formula> (<inline-formula><tex-math id="M3">$ a,b,r\in {\mathbb{C}} $</tex-math></inline-formula>) of rank three with free <inline-formula><tex-math id="M4">$ {\mathbb{C}}[{\partial}] $</tex-math></inline-formula>-basis <inline-formula><tex-math id="M5">$ \{L, W,Y\} $</tex-math></inline-formula> and relations <inline-formula><tex-math id="M6">$ [L_{\lambda} L] = ({\partial}+2{\lambda})L,\ [L_{\lambda} W] = ({\partial}+ a{\lambda} +b)W,\ [L_{\lambda} Y] = ({\partial}+{\lambda})Y,\ [Y_{\lambda} W] = rW $</tex-math></inline-formula> and <inline-formula><tex-math id="M7">$ [Y_{\lambda} Y] = [W_{\lambda} W] = 0 $</tex-math></inline-formula>. In this paper, we investigate the irreducibility of all free nontrivial <inline-formula><tex-math id="M8">$ \mathcal{W}(a,b,r) $</tex-math></inline-formula>-modules of rank one over <inline-formula><tex-math id="M9">$ {\mathbb{C}}[{\partial}] $</tex-math></inline-formula> and classify all finite irreducible conformal modules over <inline-formula><tex-math id="M10">$ \mathcal{W}(a,b,r) $</tex-math></inline-formula>.</p>

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Section: Definition 22 a Conformal Module M Over A Lie Conformal Almentioning

confidence: 99%

mentioning

confidence: 99%

Classification of finite irreducible conformal modules over Lie conformal algebra <inline-formula><tex-math id="M1">$ \mathcal{W}(a, b, r) $</tex-math></inline-formula>

Liu

Xiao

Yue

2021

era

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Two $$\mathbb {Z}$$-Graded Infinite Lie Conformal Algebras Related to the Virasoro Conformal Algebra

Yue,

Zou

2024

Algebr Represent Theor

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Irreducible modules over the Lie conformal algebra $${\mathfrak {B}}(\alpha ,\beta ,p)$$

Chen,

Hong,

2024

Collect. Math.

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

Cited by 10 publications

References 18 publications

Classification of finite irreducible conformal modules over Lie conformal algebra <inline-formula><tex-math id="M1">$ \mathcal{W}(a, b, r) $</tex-math></inline-formula>

Classification of finite irreducible conformal modules over Lie conformal algebra <inline-formula><tex-math id="M1">$ \mathcal{W}(a, b, r) $</tex-math></inline-formula>

Two $$\mathbb {Z}$$-Graded Infinite Lie Conformal Algebras Related to the Virasoro Conformal Algebra

Irreducible modules over the Lie conformal algebra $${\mathfrak {B}}(\alpha ,\beta ,p)$$

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