Loop Heisenberg-Virasoro Lie conformal algebra

Let HV be the loop Heisenberg-Virasoro Lie algebra over C with basis {L-alpha,L-i, H-beta,H-j vertical bar alpha, beta, i, j is an element of Z} and brackets [L-alpha,L-i, L-beta,L-j] = (alpha - beta) L-alpha+beta,L-i+j, [L-alpha,L-i, H-beta,H-j] = -beta H-alpha+beta,H-i+j, [H-alpha,H-i, H-beta,H-j] = 0. In this paper, a formal distribution Lie algebra of HV is constructed. Then, the associated conformal algebra CHV is studied, where CHV has a C[partial derivative]-basis {L-i, H-i vertical bar i is an element of Z} with lambda-brackets [L-i (lambda) L-j] = (partial derivative + 2 lambda) Li+j, [L-i lambda H-j] = (partial derivative + lambda)Hi+j, [H-i lambda L-j] = lambda Li+j, and [H-i lambda H-j] = 0. In particular, the conformal derivations of CHV are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CHV are classified. (C) 2014 AIP Publishing LLC.