Hi,(adsbygoogle = window.adsbygoogle || []).push({});

theabelianizationof a group G is given by the quotient G/[G,G], where [G,G] is thecommutatorsubgroupof G. When dealing with finite groups, the commutator subgroup is given by the (normal) subgroup generated by all the commutators of G.

If we consider instead the case of G being a Lie group, how do we abelianize it? In particular, do we define the commutator subgroup of a Lie group G in the standard way, as all the elements of G obtained by finite sequences of commutators and their inverses?

Thanks.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Abelianization of Lie groups

Loading...

Similar Threads - Abelianization groups | Date |
---|---|

I Group theory in physics | Mar 27, 2017 |

I Free Abelian Groups ... Aluffi Proposition 5.6 | May 13, 2016 |

Finding non-trivial automorphisms of large Abelian groups | May 30, 2015 |

Groups of homomorphisms of abelian groups | Oct 10, 2014 |

**Physics Forums - The Fusion of Science and Community**