Abstract
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.
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