Extensions of conformal modules over Lie conformal algebras of Block type

Abstract

We classify extensions between finite irreducible conformal modules over a class of infinite Lie conformal algebras B(p) of Block type, where p is a nonzero complex number. We find that although certain finite irreducible conformal modules over B(p) are simply conformal modules over its Virasoro conformal subalgebra Vir, there exist more nontrivial extensions between these conformal B(p)-modules. For extensions between other conformal modules, the situation becomes rather different. As an application, we also solve the extension problem for a series of finite Lie conformal algebras b(n) for n≥1.