Journal of Lie Theory 34 (2024), No. 1, 001--016
Copyright Heldermann Verlag 2024
Nonabelian Tensor Squares of Compact Groups via Quotients of Free Compact Groups
Mita Ramabulana
Dept. of Mathematics and Applied Mathematics, University of Cape Town, Cape Town, South Africa
ramabulanamd@gmail.com
Francesco G. Russo
Dept. of Mathematics and Applied Mathematics, University of Cape Town, Cape Town, South Africa
francescog.russo@yahoo.com
We provide an explicit construction for the nonabelian tensor square of compact groups in terms of quotients of free compact groups. This has several consequences in terms of structural results and, just to mention two of them, one is a new upper bound for the weight of the nonabelian tensor square, another is the description of complements for the nonabelian tensor squares when we focus on the case of pro-p-groups.
Keywords: Compact groups, nonabelian exterior square, Schur multiplier, varieties of topological groups, free groups.
MSC: 22C05, 20E18, 20J05, 20J06.
[ Fulltext-pdf (171 KB)] for subscribers only.