Extensions of finite irreducible conformal modules over Lie conformal algebras (a,b,r).

In this article, we study extensions of conformal modules over Lie conformal algebras W (a , b , r) with three parameters a, b, r ∈ C , which contain the Virasoro Lie conformal algebra Vir, W (b) and W (a , b) as subalgebras. We obtain the existence conditions of extensions of nontrivial conformal modules over W (a , b , r) and give a complete classification of extensions of finite irreducible conformal modules of W (a , b , r) . [ABSTRACT FROM AUTHOR]