Journal of Lie Theory 28 (2018), No. 1, 169--185
Copyright Heldermann Verlag 2018
The Non-Abelian Tensor and Exterior Products of Crossed Modules of Lie Algebras
Hajar Ravanbod
Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
hajarravanbod@gmail.com
Ali Reza Salemkar
Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
salemkar@sbu.ac.ir
The notions of non-abelian tensor and exterior products of two ideal crossed submodules of a given crossed module of Lie algebras are introduced and some of their fundamental properties are established. Using the obtained results, we also give a new description of the second homology of Lie algebra crossed modules.
Keywords: Lie algebra, crossed module, tensor product, exterior product.
MSC: 18G05, 18G50, 20J99
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