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 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.
For any complex parameters a, b, let [Formula: see text] be the Lie algebra with basis {Li,Hi | i ∈ ℤ} and relations [Li,Lj]=(j-i)Li+j, [Li,Hj]=(a+j+bi)Hi+j and [Hi,Hj]=0. In this paper, we construct the [Formula: see text] conformal algebra for some a, b and its conformal module of rank one.
Let L be a Lie algebra of Block type over C with basis {L α,i | α, i ∈ Z} and brackets [L α,i , L β,j ] = (β(i + 1) − α(j + 1))L α+β,i+j . In this paper, we shall construct a formal distribution Lie algebra of L. Then we decide its conformal algebra B with C[∂]-basis {L α (w) | α ∈ Z} and λ-brackets [L α (w) λ L β (w)] = (α∂ + (α + β)λ)L α+β (w). Finally, we give a classification of free intermediate series B-modules.
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