Compatible anti-pre-Lie algebras

In this paper, we introduce the notion of compatible anti-pre-Lie algebras and study relationship between them and the related structures such as anti-[Formula: see text]-operators, commutative [Formula: see text]-cocycles on compatible Lie algebras. Moreover, we give the classification of 2-dimensional compatible anti-pre-Lie algebras from the classification of anti-pre-Lie algebras of the same dimension.