预李代数的交叉模

Journal of Jilin University Science Edition ›› 2022, Vol. 60 ›› Issue (3): 604-608.

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Crossed Module of Pre-Lie Algebras

SUN Jubo¹, ZHANG Qingcheng²

1. Faculty of Applied Sciences, Jilin Engineering Normal University, Changchun 130052, China;
2. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Received:2021-08-23 Online:2022-05-26 Published:2022-05-26

Abstract

Abstract: Firstly, we gave the definitions of the action and the crossed module of pre-Lie algebras, and studied the related properties of the
crossed module. Secondly, a result was given that the isomorphism class of crossed modules of pre-Lie algebra was equivatent to that of cat¹-pre-Lie algebras by using the definition of the crossed modules and semidirect product of pre-Lie algebras. Finally, we showed that the homomorphisms and their homotopies of crossed module formed a groupoid structure.

Key words: pre-Lie algebra, crossed module, action, homomorphism, groupoid

CLC Number:

O152.5

SUN Jubo, ZHANG Qingcheng. Crossed Module of Pre-Lie Algebras[J].Journal of Jilin University Science Edition, 2022, 60(3): 604-608.

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Crossed Module of Pre-Lie Algebras

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