Does any one know if there is a way of constructing a non-Abelian Lie Group from Abelian Lie groups beyond using a semi-direct product?

I don't think so but there may be some pathological cases or obscure theorem out there.

Thank you in advance.

  • $\begingroup$ What do you mean by "from"? $\endgroup$ – Igor Rivin Mar 5 '18 at 2:43
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    $\begingroup$ Ok, that is not good wording. What I mean is: can I construct a non-Abelian Lie group using (? better wording) abelian groups some how. i.e. one possibility is using a semi-direct product of abelian groups to form an non-Abelian group. But I am wondering if there is another alternative. $\endgroup$ – SAMCRO Mar 5 '18 at 2:45
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    $\begingroup$ Yes, you can consider extensions that are not semidirect products. $\endgroup$ – Pedro Tamaroff Mar 5 '18 at 2:46
  • $\begingroup$ Thank you, could you possibly direct me to an example or reference please? $\endgroup$ – SAMCRO Mar 5 '18 at 2:50

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