Infinite rank Schrödinger-Virasoro type Lie conformal algebras

Abstract

Motivated by the structure of certain modules over the loop Virasoro Lie conformal algebra and the Lie structures of Schrödinger-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.