
Journal of Lie Theory 31 (2021), No. 4, 933956 Copyright Heldermann Verlag 2021 A NonAbelian 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 nonabelian 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. [ Fulltextpdf (217 KB)] for subscribers only. 