On Schr\"odinger-Virasoro type Lie conformal algebras

TL;DR

This paper introduces two new classes of Schr"odinger-Virasoro type Lie conformal algebras, analyzes their structure, and determines their central extensions, conformal derivations, and rank 1 modules.

Contribution

It presents novel non-simple Schr"odinger-Virasoro type Lie conformal algebras and characterizes their algebraic properties and modules.

Findings

Defined two new classes TSV(a,b) and TSV(c)

Determined central extensions and conformal derivations

Classified free conformal modules of rank 1

Abstract

In this paper, two new classes of Schr\"{o}dinger-Virasoro type Lie conformal algebras TSV(a,b) and TSV(c) which are non-simple are introduced for some a, b, c\in \mathbb{C}. Moreover, central extensions, conformal derivations and free conformal modules of rank 1 of TSV(a,b) and TSV(c) are determined.