Cohomology of the Schrödinger-Virasoro Lie conformal algebras TSV(a,b) and TSV(c)

In this paper, we study two types of Schrödinger-Virasoro Lie conformal algebras TSV(a,b) and TSV(c), which are important rank three nonsimple Lie conformal algebras. We completely determine the basic and reduced cohomology groups of TSV(a,b) with coefficients in its trivial module for the case of a∈{a<2|a∈Q}∪(C−Q) and b=0 as well as the low-dimensional basic cohomology groups of TSV(a,b) with trivial coefficients for a∈C and b=0. Furthermore, we determine the reduced cohomology groups of TSV(a,b) with coefficients in its rank one nontrivial irreducible module Mα,β. Finally, we provide the similar conclusions for TSV(c).