Journal of Lie Theory 31 (2021), No. 4, 933--956
Copyright Heldermann Verlag 2021
A Non-Abelian Tensor Product of Lie Crossed Modules
Arash Javan
Dept. of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
a_javan@sbu.ac.ir
Hajar Ravanbod
Dept. of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
hajarravanbod@gmail.com
Ali Reza Salemkar
Dept. of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
salemkar@sbu.ac.ir
The notions of non-abelian tensor and exterior products in the category of Lie crossed modules are introduced and investigated. Also, their relationships with the Whitehead's universal quadratic and the homology of Lie crossed modules are established.
Keywords: Lie algebra, crossed module, tensor product, exterior product.
MSC: 17B05, 17B99, 18G50, 18G99.
[ Fulltext-pdf (217 KB)] for subscribers only.