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arXiv · 2306.12425

Cohomologies of pre-LieDer pairs and applications

Shanshan Liu·Liangyun Chen
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Abstract

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 $L_\infty$-algebra of this controlling algebra. In particular, we define the cohomology of regular pre-LieDer pairs. We study infinitesimal deformations of pre-LieDer pairs, which are characterized by the second cohomology group of pre-LieDer pairs. We also define the cohomology of regular pre-LieDer pairs with coefficients in arbitrary representation and using the second cohomology group to classify abelian extensions of regular pre-LieDer pairs.

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Shanshan Liu, Liangyun Chen. 2023-03-08. Cohomologies of pre-LieDer pairs and applications. https://arxiv.org/abs/2306.12425

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