The Lie conformal algebra of loop Virasoro algebra, denoted by C W , is introduced in this paper. Explicitly, C W is a Lie conformal algebra withThen conformal derivations of C W are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over C W are classified.

In this paper, we classify all finite irreducible conformal modules over a class of Lie conformal algebras W(b) with b ∈ C related to the Virasoro conformal algebra. Explicitly, any finite irreducible conformal module over W(b) is proved to be isomorphic to M ∆,α,β with ∆ = 0 or β = 0 if b = 0, or M ∆,α with ∆ = 0 if b = 0. As a byproduct, all finite irreducible conformal modules over the Heisenberg-Virasoro conformal algebra and the Lie conformal algebra of W(2, 2)-type are classified. Finally, the same thing is done for the Schrödinger-Virasoro conformal algebra.

Let HV be the loop Heisenberg-Virasoro Lie algebra over C with basisIn this paper, a formal distribution Lie algebra of HV is constructed. Then the associated conformal algebra CHV is studied, where CHV has a C[∂ ]-basisIn particular, the conformal derivations of CHV are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CHV are classified.

In this article, we study the structure theory of a class of generalized loop Virasoro algebras. In particular, the derivation algebras, the automorphism groups, and the second cohomology groups of generalized loop centerless Virasoro algebras are determined.

Abstract:The purpose of this paper is to study W .2; 2/ Lie conformal algebra, which has a free COE@ -basisIn this paper, we study conformal derivations, central extensions and conformal modules for this Lie conformal algebra. Also, we compute the cohomology of this Lie conformal algebra with coefficients in its modules. In particular, we determine its cohomology with trivial coefficients both for the basic and reduced complexes.