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math.RA2023★ 1 cited
Cohomologies of pre-LieDer pairs and applications
Shanshan Liu, Liangyun Chen
In this paper, we use the higher derived bracket to give the controlling algebra of pre-LieDer pairs. We give the cohomology of pre-LieDer pairs by using the twist -algeb…
math.RA2023
Deformations and abelian extensions of compatible pre-Lie algebras
Shanshan Liu, Liangyun Chen
In this paper, we first give the notation of a compatible pre-Lie algebra and its representation. We study the relation between compatible Lie algebras and compatible pre-Lie algeb…
math.RA2023
Deformations and abelian extensions on anti-pre-Lie algebras
Shanshan Liu, Zhao Chen, Liangyun Chen
In this paper, we introduce the representation of anti-pre-Lie algebras and give the second cohomology group of anti-pre-Lie algebras. As applications, first, we study linear defor…