Classification of finite irreducible conformal modules over some Lie conformal algebras related to the Virasoro conformal algebra

Abstract

In this paper, we classify all finite irreducible conformal modules over a class of Lie conformal algebras $\mathcal{W}(b)$ with $b\in \mathbb{C}$ related to the Virasoro conformal algebra. Explicitly, any finite irreducible conformal module over $\mathcal{W}(b)$ is proved to be isomorphic to $M_{\Delta ,\alpha ,\beta }$ with $\Delta \ne 0$ or $\beta \ne 0$ if $b=0$, or $M_{\Delta ,\alpha }$ with $\Delta \ne 0$ if $b\ne 0$. As a byproduct, all finite irreducible conformal modules over the Heisenberg-Virasoro conformal algebra and the Lie conformal algebra of $\mathcal{W}(2,2)$-type are classified. Finally, the same thing is done for the Schrödinger-Virasoro conformal algebra.

References in corpus (4)

• SCHRÖdinger Invariance and Strongly Anisotropic Critical Systems
• Schr"odinger invariance and space-time symmetries
• Cohomology of Conformal Algebras
• Cohomology of Heisenberg-Virasoro conformal algebra

Cited by in corpus (6)

• Extensions of Schrödinger-Virasoro conformal modules
• Finite irreducible conformal modules over the Lie conformal superalgebra $\mathcal{S}(p)$
• On structured spaces and their properties
• Extensions of finite irreducible modules of Lie conformal algebras $\mathcal{W}(a,b)$ and some Schrödinger-Virasoro type Lie conformal algebras
• Conformal modules and their extensions of a Lie conformal algebra related to a 2-dimensional Novikov algebra
• Finite irreducible modules of Lie conformal algebras $\mathcal{W}(a,b)$ and some Schrödinger-Virasoro type Lie conformal algebras