Derivations, 2-local derivations, biderivations and automorphisms of the generalized loop Heisenberg-Virasoro algebra

In this paper, the generalized Loop Heisenberg-Virasoro algebra is introduced. Firstly, we determine the derivations on the generalized Loop Heisenberg-Virasoro algebra. Then we show that all 2-local derivations are derivations. Furthermore, we determine the biderivations on the generalized Loop Heisenberg-Virasoro algebra are inner biderivations and give their applications. Finally, the automorphism groups on the generalized Loop Heisenberg-Virasoro algebra are presented.