Extensions and Crossed Modules of n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{n}$$\end{document}-Lie–Rinehart Algebras

被引:0
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作者
A. Ben Hassine
T. Chtioui
M. Elhamdadi
S. Mabrouk
机构
[1] University of Bisha,Department of Mathematics, College of Science and Arts at Belqarn
[2] University of Sfax,Faculty of Sciences
[3] University of South Florida,Department of Mathematics
[4] University of Gafsa,Faculty of Sciences
关键词
-Lie–Rinehart algebras; -Lie algebroids; Representations; Cohomology; Extensions; Crossed modules; 17A42; 17A30; 53D17; 17A32;
D O I
10.1007/s00006-022-01218-y
中图分类号
学科分类号
摘要
We introduce a notion of n-Lie–Rinehart algebras as a generalization of Lie–Rinehart algebras to n-ary case. This notion is also an algebraic analogue of n-Lie algebroids. We develop representation theory and describe a cohomology complex of n-Lie–Rinehart algebras. Furthermore, we investigate extension theory of n-Lie–Rinehart algebras by means of 2-cocycles. Finally, we introduce crossed modules of n-Lie–Rinehart algebras to gain a better understanding of their third cohomology groups.
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