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 (3)

• Representations of simple finite Lie conformal superalgebras of type W and S
• Loop Heisenberg-Virasoro Lie Conformal algebra
• Filtered Lie conformal algebras whose associated graded algebras are isomorphic to that of general conformal algebra $g{c}_1$

Cited by in corpus (1)

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