Journal of Lie Theory

no. 1
Nonabelian Tensor Squares of Compact Groups via Quotients of Free Compact Groups
Mita Ramabulana1; Francesco G. Russo1
1Dept. of Mathematics and Applied Mathematics, University of Cape Town, Cape Town, South Africa
Journal of Lie Theory, Volume 34 (2024) no. 1, pp. 1-16
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.
DOI: 10.5802/jolt.1324
Classification: 22C05, 20E18, 20J05, 20J06
Keywords: Compact groups, nonabelian exterior square, Schur multiplier, varieties of topological groups, free groups

Mita Ramabulana  1 ; Francesco G. Russo  1

1 Dept. of Mathematics and Applied Mathematics, University of Cape Town, Cape Town, South Africa 
Mita Ramabulana; Francesco G. Russo. Nonabelian Tensor Squares of Compact Groups via Quotients of Free Compact Groups. Journal of Lie Theory, Volume 34 (2024) no. 1, pp. 1-16. doi: 10.5802/jolt.1324
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