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

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