Compatible anti-pre-Lie algebras

Abstract

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-O-operators, commutative 2-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.

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