Infinite rank Schrodinger-Virasoro type Lie conformal algebras

TL;DR

This paper constructs and classifies a new class of infinite rank Lie conformal algebras inspired by the structure of modules over loop Virasoro and Schrodinger-Virasoro algebras, analyzing their derivations and modules.

Contribution

It introduces the CSV (a, b) Lie conformal algebras, determines their conformal derivations, and classifies their rank one modules and intermediate series modules.

Findings

Conformal derivations of CSV (a, b) are uniformly determined.

Rank one conformal modules over CSV (a, b) are classified.

Z-graded free intermediate series modules are classified.

Abstract

Motivated by the structure of certain modules over the loop Virasoro Lie conformal algebra and the Lie structures of Schrodinger-Virasoro algebras, we construct a class of infinite rank Lie conformal algebras CSV (a, b), where a, b are complex numbers. The conformal derivations of CSV (a, b) are uniformly determined. The rank one conformal modules and Z-graded free intermediate series modules over CSV (a, b) are classified. Corresponding results of the conformal subalgebra CHV (a, b) of CSV (a, b) are also presented.