Finite irreducible conformal modules over the Lie conformal superalgebra $\mathcal{S}(p)$

Abstract

In the present paper, we introduce a class of infinite Lie conformal superalgebras $\mathcal{S}(p)$, which are closely related to Lie conformal algebras of extended Block type defined in \cite{CHS}. Then all finite non-trivial irreducible conformal modules over $\mathcal{S}(p)$ for $p\in\C^*$ are completely classified. As an application, we also present the classifications of finite non-trivial irreducible conformal modules over finite quotient algebras $\mathfrak{s}(n)$ for $n\ge 1$ and $\mathfrak{sh}$ which is isomorphic to a subalgebra of Lie conformal algebra of $N=2$ superconformal algebra. Moreover, as a generalized version of $\mathcal{S}(p)$, the infinite Lie conformal superalgebras $\mathcal{G}\mathcal{S}(p)$ are constructed, which have a subalgebra isomorphic to the finite Lie conformal algebra of $N=2$ superconformal algebra.

References in corpus (12)

• Cohomology of Conformal Algebras
• Formal distribution algebras and conformal algebras
• Finite conformal modules over the N=2,3,4 superconformal algebras
• Loop Virasoro Lie Conformal Algebra
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• Classification of finite irreducible conformal modules over some Lie conformal algebras related to the Virasoro conformal algebra
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• Irreducible modules over finite simple Lie conformal superalgebras of type K
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• On the quantum super Virasoro algebra
• Filtered Lie conformal algebras whose associated graded algebras are isomorphic to that of general conformal algebra $g{c}_1$
• Finite irreducible conformal modules over the extended Block type Lie conformal algebra $\mathfrak{B}(\alpha ,\beta ,p)$

Cited by in corpus (1)

• Lie conformal superalgebras and duality of modules over linearly compact Lie superalgebras