2023/03/08 by Shanshan Liu, Liangyun Chen, Liu, Shanshan +1
Mathematics · Medicine · #Advanced Topics in Algebra #FOS: Mathematics #Ophthalmology and Eye Disorders #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2306.12425
openalex publication_date 2023/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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_∞-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.