Schrödinger-Virasoro Lie conformal algebra

Abstract

We first construct two new nonsimple conformal algebras associated with the Schrödinger-Virasoro Lie algebra and the extended Schrödinger-Virasoro Lie algebra, respectively. Then we study conformal derivations and free nontrivial rank one conformal modules of these two conformal algebras. Also, we provide a computation of their universal central extensions.

Extensions of Schrödinger–Virasoro conformal modules

“…In particular, λ -brackets arise as generating functions for the singular part of the OPE. The structure, cohomology and representation theory of LCAs was developed by V. Kac and his coworkers in the late 1990s ( [1][2][3][4][5][6]), and non-semisimple LCAs associated to infinitedimensional Lie algebras of Virasoro type were studied recently in [10][11][12][13][14][15]. As pointed out in [2], conformal modules of LCAs are not completely reducible in general.…”

“…In this paper, we aim to study extensions of modules over the Schrödinger-Virasoro conformal algebra and the extended Schrödinger-Virasoro conformal algebra, which were introduced in [10] as Lie conformal algebras associated to the Schrödinger-Virasoro Lie algebra and the extended Schrödinger-Virasoro Lie algebra, respectively. The Schrödinger-Virasoro conformal algebra is defined as a finite free Lie conformal Therefore, the classification of extensions of Virasoro conformal modules obtained in [3] will be used in our study, and one will see that our result can be directly applied to the Heisenberg-Virasoro conformal algebra.…”

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

“…In this paper, we investigate extensions of finite irreducible conformal modules of Lie conformal algebras W(a, b), T SV (a, b) and T SV (c), where W(a, b) is a semi-direct sum of V ir and its nontrivial conformal modules of rank one, T SV (a, b) and T SV (c) are two classes of Schrödinger-Virasoro type Lie conformal algebras introduced in [7]. Note that W(1 − b, 0) is just the Lie conformal algebra W(b) in [18], W(1, 0) is just the Heisenberg-Virasoro Lie conformal algebra, T SV ( 3 2 , 0) is just the Schrödinger-Virasoro Lie conformal algebra in [15] and T SV (0, 0) is just the Schrödinger-Virasoro type Lie conformal algebra in [16]. Finite irreducible conformal modules of W(1, 0) and W(1 − b, 0) were classified in [17].…”

Infinite rank Schrödinger-Virasoro type Lie conformal algebras

“…The simplest but rather important finite Lie conformal algebra is the Virasoro conformal algebra, whose irreducible conformal modules were classified in [6]. More recently, some finite Lie conformal algebras related to the Virasoro conformal algebra have been constructed and studied, such as Schrödinger-Virasoro type Lie conformal algebras [11,16,18] and W (a, b)…”

“…which was studied in [11]. The special cases SV (1, 0) and SV (−2, 0) were firstly considered in [16] and [18], respectively. Furthermore, SV (a, b) contains a Virasoro conformal subalgebra CVir = C[∂]L 0 , and a finite Heisenberg-Virasoro type conformal subalgebra…”