Extensions of modules over the Heisenberg–Virasoro conformal algebra

Abstract

In this paper, extensions between finite conformal modules over the Heisenberg–Virasoro conformal algebra are classified.

Extensions of Schrödinger–Virasoro conformal modules

“…By Lemma 5.5 and Theorems 5.9-5.10, we have Remark 6.4. We studied extensions of Heisenber-Virasoro conformal modules in [8]. However, there exist some mistakes in the main results.…”

Finite irreducible modules of Lie conformal algebras 𝒲(a,b) and some Schrödinger–Virasoro type Lie conformal algebras

“…Actually, W(1, 0) is the Heisenberg-Virasoro conformal algebra. Moreover, extensions of finite irreducible modules over it were classified in [12,19]. So we will give their results directly below without proof.…”

“…In [11], we gave a complete classification of finite irreducible conformal modules of W(a, b), T SV (a, b) and T SV (c). In [12,13,19], Ling and Yuan classified all extensions of finite irreducible conformal modules over W(1, 0) , W(1 − b, 0) and T SV ( 3 2 , 0). In this paper, we deal with the same problem for W(a, b), T SV (a, b) and T SV (c).…”

Extensions of modules over a class of Lie conformal algebras 𝒲(b)

“…In this paper, we will consider extensions of conformal W (b)-modules with b = 0, since this problem for W (0)-modules have been solved in [6]. The rest paper is organized as follows.…”