On Heisenberg-Virasoro pseudoalgebras

In this paper, we introduce and study a class of neither simple nor semi-simple Lie H-pseudoalgebras which can be seen as an extension of the primitive pseudoalgebras of vector fields H(δ, χ, ω) or K(δ, θ). In particular, we investigate the rank one modules, derivations and cohomology groups on Heisenberg-Virasoro pseudoalgebras, a class of special cases of Lie H-pseudoalgebras.