Vladimir Kovalchuk constructed a two parameter family of VOA that have an affine sp(2) as subalgebra and in each even positive conformal weight a singlet and at each odd one an sp(2)-triplet. This structure is the third universal family of W-algebras after the W-infinity algebra and its even spin analogue and quotients of one-parameter subfamilies of Vladimir algebras are often realized by cosets of certain W-algebras of orthosymplectic type. Very much like in the W-infinity case and in the even spin case it is expected that there are quotients that are rational and lisse. I will explain that this expectation is indeed true and it is given by a novel family of rational and lisse cosets. This is joint work with Vlad Kovalchuk and Andy Linshaw.

In this talk I will discuss M(A), the multiplier algebra of a general Banach algebra A, as well as some of its properties. I will present a main result that produces an isometric representation of M(A) on a Banach space E whenever A has a contractive approximate identity (cai) and a nondegenerate isometric representation on E. This implies that the multiplier algebra of a "C*-like" L^p-operator algebra is again an L^p-operator algebra. I will then focus on some particular degenerate L^p operator algebras without cai's and say something about their multiplier algebras.