Loop Heisenberg-Virasoro Lie conformal algebra

Abstract

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.

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 W(a,b) Lie conformal algebra

“…For simplicity, we denote by C ∞ the space of such conformal derivations. Methods similar to those in the article [7] are used to discuss nonzero parameter b. As a result, we obtain the following theorem.…”

“…For example, the conformal subalgebra CVir = C[∂ ]L 0 is isomorphic to the well-known Virasoro conformal algebra and the conformal subalgebra CW = i∈Z C[∂ ]L i is isomorphic to the loop Virasoro Lie conformal algebra studied in [25]. Furthermore, we know that CLW (0, 0) is the loop Heisenberg-Virasoro Lie conformal algebra which was studied in [7]. In addition, [26] constructed the W (a, b) Lie conformal algebra for some a, b and its conformal module of rank one.…”

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].…”