首页|Cohomologies and crossed modules for pre-Lie Rinehart algebras

Cohomologies and crossed modules for pre-Lie Rinehart algebras

扫码查看
原文链接
  • NSTL
  • Elsevier
A pre-Lie-Rinehart algebra is an algebraic generalization of the notion of a left-symmetric algebroid. We construct pre-Lie-Rinehart algebras from r-matrices through Lie algebra actions. We study cohomologies of pre-Lie-Rinehart algebras and show that abelian extensions of pre-Lie-Rinehart algebras are classified by the second cohomology groups. We introduce the notion of crossed modules for pre-Lie-Rinehart algebras and show that they are classified by the third cohomology groups of pre-Lie-Rinehart algebras. At last, we use (pre-)Lie-Rinehart 2-algebras to characterize the crossed modules for (pre-)Lie Rinehart algebras. (C) 2022 Elsevier B.V. All rights reserved.

Pre-Lie-Rinehart algebraCohomologyAbelian extensionCrossed module(Pre-)Lie-Rinehart 2-algebra

Chen, Liangyun、Liu, Meijun、Liu, Jiefeng

展开 >

Northeast Normal Univ

2022

10.1016/j.geomphys.2022.104501

Journal of geometry and physics

Journal of geometry and physics

SCI
ISSN：0393-0440
年,卷(期)：2022.176
  • 28