2-Local derivations of Heisenberg–Virasoro type Lie algebras

Let Formula: see text with Formula: see text be the Heisenberg–Virasoro type Lie algebras, and Formula: see text be a thin Lie algebra with only one diamond. In this paper, we study Formula: see text-local derivations on Formula: see text and Formula: see text. For Formula: see text, we show that every Formula: see text-local derivation is a derivation for almost all parameter pairs Formula: see text, generalizing some previous results, while for Formula: see text, we show that it admits infinite many Formula: see text-local derivations which are not derivations. Along the way, we also prove that the space of outer derivations of Formula: see text is infinite-dimensional.