Loop Virasoro Lie conformal algebra

Abstract

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.

Classification of finite irreducible conformal modules over a class of Lie conformal algebras of Block type

“…Due to these reasons, the general Lie conformal algebra gc N and its subalgebras have been studied by many authors (e.g., [3,4,6,9,10,21,25,29]). Recently, some interesting examples of infinite Lie conformal algebras associated with infinite-dimensional loop Lie algebras were constructed and studied (e.g., [12,13,26]).…”

Loop Virasoro Lie conformal superalgebra

“…(i) We only restrict ourself to the irreducibility of M a,b,c , the other one can be treated similarly. It is clear that x as an clv-module (see [8,16]), we can obtain that…”

“…We cite the classification result of nontrivial free Z-graded clv-modules of rank one from [16] as a lemma here.…”

“…Note that this is an infinite simple Lie conformal superalgebra, containing the loop Virasoro Lie conformal algebra clv = i∈Z C[∂]L i (see [16]) as its subalgebra. As pointed out previously, the theory of finite simple Lie conformal (super)algebras were well developed, but so far there is no systematic theory for the infinite case.…”

Structure of a class of Lie conformal algebras of Block type

“…For example, the finite irreducible conformal modules over gc N were classified by Kac, Radul and Wakimoto, see also [2,9]; the finite growth modules over subalgebras of gc N containing Virasoro conformal subalgebras were classified in [2]; certain low dimensional cohomologies of gc N were computed in [10]. Recent years, some infinite rank loop * -Virasoro type Lie conformal algebras were constructed and studied, such as the loop Virasoro type [15], Heisenberg-Virasoro type [7] and Schrödinger-Virasoro type [8].…”